The CAT exam for MBA admissions is expected to take place in November 2025. In this 60-day CAT 2025 preparation guide series by Careers360, we’ll discuss strategies for tackling Permutation and Combination problems on Day 37, helping you prepare effectively and succeed in the CAT entrance test.
CAT 2025 Permutation and Combination Problems, Syllogism Tricks With Solutions
This article covers permutation and combination problems, syllogism questions with answers, and tips for understanding comparison in VARC. Permutation and combination problems are often considered challenging, and many aspirants struggle with them. To aid your preparation, we've included Permutation and Combination examples with answers, as well as previous years' questions (PYQs) for practice.
CAT Exam Important Topic: Strategy to Prepare Permutation and Combination (Selection, Grouping and Distribution) and permutation and combination problems.
Permutation and combination problems
The number of permutations of n distinct items taking r items at a time is
nPr = n!/n-r!
nPn = n!
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Previous Year CAT Questions on Permutations and Combinations (Selections and Groupings, Distributions):
Q1. The number of ways of distributing 15 identical balloons, 6 identical pencils and 3 identical erasers among 3 children, such that each child gets at least four balloons and one pencil, is [TITA, CAT 2021 Slot-2]
Given that, there are 15 identical balloons, 6 identical pencils, and 3 identical erasers.
We need to distribute these items among 3 children, such that each child gets at least four balloons and one pencil.
First, distribute 4 balloons and 1 pencil to each child. Now, we have 3 balloons, 3 pencils, and 3 erasers left with us after distribution.
Remaining balloons can be distributed in following possible combination;
(3, 0, 0), (2, 1, 0), (1, 1, 1)
(3, 0, 0) can be arranged in three ways.
(2, 1, 0) can be arranged in six ways.
(1, 1, 1) can be arranged in only one way.
The total ways of distributing the remaining balloons are 6+ 3+ 1= 10 ways.
Similarly, we can arrange 3 pencils in 10 ways and 3 erasers in 10 ways.
Therefore, the total number of ways is 10 x 10 x 10 = 1000 ways
Permutation and Combination Aptitude
Q2. In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser. Still, nobody gets more than 3 erasers? [CAT 2017]
16
20
14
15
Permutation and combination examples with answers
Ans: A
We have to find by how many numbers of ways the erasers are distributed such that each kid gets at least one eraser but nobody gets more than 3 erasers.
4 kids are getting a, b, c, d erasers such that a + b + c + d = 7.
a = p+1
b = q+ 1
c = x+ 1
d = z+1 since each should have at least 1 eraser.
So, p + q+ x+ y = 3
number of ways of distribution = n+rCr-1; here n =3, r = 4(number of variables)
So, the number of ways of distribution = 6C3 = 20 ways
If one kid a, gets 4 erasers the other kids b, c, and d can get each one respectively such that 4, 1, 1, 1 or 1, 1, 1, 4 or 1, 4, 1, 1 or 1, 1, 4, 1 so there are chances of 4 ways.
So, required ways = 20 – 4 = 16 ways
CAT entrance exam: Pre-requisite to permutation and combination problems
Part-2: CAT 2025 Preparation Tips: CAT DILR tips (Logical Reasoning and Data Interpretation)
CAT 2025 Syllabus Topic: Strategy to prepare “Syllogism through PYQs” (Part-2) and syllogism reasoning questions and Syllogism examples with answers
CAT Exam:
Previous Year CAT Questions on Syllogism from CAT/ MBA Entrance Exam:
Q1. The following question is given by 3 statements and 2 conclusions numbered I and II. Choose the right answer from the given options. [MAHCET MBA 2024]
Statements:
I. No Box is a Book.
II. Few cups are books.
III. Only a few knives are Boxes.
Conclusions:
I. Some Knives being a book is a possibility.
II. All Cups being a Book is a possibility.
If only conclusion I follows
If only conclusion II follows
If either I or II follows
If neither I nor II follows
If both conclusions follow
Solution: [E]
Cat Tips for syllogism 1: Draw Venn Diagram first
Cat Tips for syllogism 2: ‘A few’ means ‘some’
Cat Tips for syllogism 3: Go through Conclusions.
Conclusion 1: Some Knives being a book is a possibility.
Some Knives are there which are not certain to be either Boxes or Books. Therefore, Some knives can be book. So, first will follow.
Conclusion 2: All Cups being a Book is a possibility.
All cups can be inside Book. So, this is a possibility. Therefore, II will follow.
Syllogism examples with answers
Q2.
Statements
i) Some Cubes are Circles.
ii) No Circle is a Triangle.
iii) No line is a Cube.
Conclusions:
i) All Cubes can never be triangles.
ii) Some lines are Circles.
iii) No triangle is a cube.
iv) No line is a circle.
All follows
I, II and III follow
I, IV and III follow
II, IV and III follow
None of these
Solution: (E)
Cat Tips for syllogism 1: Draw Venn Diagram first
Cat Tips for syllogism 2: Go through Conclusions.
i) All Cubes can never be triangles: Some cubes are Circles. So, definitely, some cubes are there which can never be Triangle.
Therefore, (i) will follow.
ii) Some lines are Circles: Not a definite conclusion; it will not follow.
iii) No triangle is a cube: Not a definite conclusion; it will not follow.
iv) No line is a circle: Not a definite conclusion; it will not follow.
Clearly, the third statement will follow.
CAT entrance exam: Prerequisite to syllogism reasoning questions
CAT does not directly repeat questions, but the same type of questions and ideas are asked annually. Number Systems, Algebra, Logical Puzzles, and Reading Comprehension topics often crop up in other forms. Working on previous year papers makes it easier for aspirants to realize the pattern of the exam and come up with improved strategies.
Q: Are mock tests important for CAT 2025 preparation?
A:
Yes, mock tests are crucial for CAT 2025 preparation since it helps the candidate, to carefully analyse their weakness and strength.
Q: What is the duration of CAT 2025 paper?
A:
The time duration for the CAT 2025 exam paper is two hours i.e. 120 minutes. The exam is conducted in different slots for the exam day.
Q: How to register for the CAT Exam 2025?
A:
To register for the CAT exam 2025, the candidate must visit the official website of the CAT. Create a login profile using e-mail ID, mobile number, and other necessary details and upload the documents required. Then finally submit the registration fees and the process is completed.
Q: When will the CAT 2025 registration start?
A:
CAT registration will start around August 2025. Candidates can start registering for the CAT exam on the official website of the CAT.
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The CAT 2025 exam is a national-level MBA entrance test for IIMs and top B-schools in India. It will be held on 30th November 2025 in computer-based mode across ~170 cities.
The registration is open from 1st August to 13th September 2025 on
iimcat.ac.in
.
Admit cards will be available from 5th November 2025 onward.
Graduates with at least 50 marks (45 for SC/ST/PwD) are eligible to apply.
The exam tests English, Reasoning, and Quantitative Aptitude in three timed sections.
With 305 marks in ICAR PG and being from ST category, your chances of getting an AIEEA (CAT) seat is good, especially in plant sciences and less competitive subjects
M/s Deloitte Touche Tohmatsu Limited, one of the top four audit and accounting firms in the world with headquarters at London, UK, and with an operational presence in 153 countries, hires Management Trainees (MT) from all the premier management institutes of India thrice every year, in the months of January, May and September.
Each new group of Management Trainees (MT) have to go through a four month rigorous training schedule, after which they have to pass through a test consisting of a written assessment and a case-analysis. The top hundred ranked Management Trainees (MT) based on the performance in the test are confirmed as Management Executives (ME). The rest are given the opportunity of undergoing the training for four months one more time along with the next batch of Management Trainees (MT) and then passing through the subsequent test consisting of the written assessment and case-analysis. The Management Trainee (MT) who fails to get confirmed as a Management Executive (ME) the second time is fired.
The scatter-graph below depicts the number of Management Trainees (MT) at Deloitte taking the tests from January 2020 till May 2022, and the vis-à-vis hired Management Trainees (MT) at Deloitte who were fired :
It is also known that for the month of September 2019 at Deloitte, 96 hired Management Trainees (MT) failed to be confirmed as a Management Executive (ME) the first time, and that 36 hired Management Trainees (MT) were fired.
Question :
In which test did the minimum number of Management Trainees (MT) get confirmed as a Management Executive (ME) in the second attempt ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the first customer's order be considered closed ?
Six sticks of equal lengths were kept in the vertical position in an empty flower-vase, to be arranged at the six corners of a regular hexagon. The two ends of each of the sticks were of different colours.
The top ends of the sticks were one of each of the following colours – Red, Cyan, Pink, Brown, Black and Green. The bottom ends were one of each of the following colours – Blue, Yellow, White, Orange, Purple and Grey. Both the sets of colours mentioned were in no particular order.
It was also known that :
a) The stick with the red colour was opposite to the stick with the blue colour
b) There were exactly two sticks whose both ends had colours whose names started with the same letter
c) The stick with the grey colour was adjacent to the stick with the white colour
d) The stick with the cyan colour was adjacent to both the sticks with the brown colour and the one with the blue colour
e) The stick with the purple colour was adjacent to both the sticks with the grey colour and the one with the green colour
f) The stick with the white colour was opposite to the stick with the green colour
Question :
What was the colour of the bottom end of the stick having brown colour at the top end ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the second customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis, when would the third customer's order be considered closed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
A fourth customer comes in and orders two plates of French Toast at 6.24 pm. Suppose Moloy and Niloy had decided to process multiple orders at the same time, however strictly prioritising a first come first serve basis. For exactly how many minutes would one of the friends be idle from 6.00 pm till serving the last customer, assuming that the four customers were the only ones to have come in within the period being discussed ?
Two friends Moloy and Niloy passed out from the Purulia Institute of Science and Technology with B.Tech degrees in Mechanical Engineering, but even after a year placement was hard to find. So they decided to take the challenge head-on, came down to Kolkata, rented a garage space on Park Street, and having an affinity towards making people enjoy good food, started their firm named 'B.Tech Bread-Omlette Wala'.
They started with three items on the menu. One was the French Toast which could be prepared in 3 minutes. The second was the Egg Tortillas which took 15 minutes to prepare. Any one of Moloy and Niloy could prepare any one of them at a time. The third was the Egg Bhurji with French Fries. This however was prepared on an automated fryer which could prepare 3 servings at a time and took 5 minutes irrespective of the number of servings equal to or below 3. The fryer did not need anyone to attend to it, and the time to put in the raw ingredients could be neglected. So one could tend to the preparation of other items while the Egg Bhurji with French Fries were being prepared.
They wanted to serve the orders as early as possible after the order was given. The individual items in any order were served as and when all the items were ready, and the order was then considered closed. None of the items on the menu were prepared in advance in anticipation of future orders.
On the first day, 3 groups of customers came in and ordered at 6.00 pm, 6.10 pm, and 6.13 pm. The first order was for a plate of Egg Tortillas, two plates of French Toast, and three plates of Egg Bhurji with French Fries. The second order was for a plate of French Toast and two plates of Egg Bhurji with French Fries. The third order was for a plate of Egg Tortilla and a plate of Egg Bhurji with French Fries.
On the backdrop of the above information answer the questions given :
Question:
Had Niloy been absent on that day, and assuming that the next customer's order could only be attended to when the previous customer's order was closed, at what time would the fourth customer's order (refer to the previous question) be considered closed ?
The bar-graph given below shows the foreign exchange reserves of Nepal (in million Rupees) from 2014 to 2021. Answer the following questions based on the graph :
Question:
What was the percentage increase (rounded to the nearest integer, if deemed necessary) in the foreign exchange reserves in 2020 over 2016 ?
The Jadavpur University’s Prince Anwar Shah Road hostel consists of two large separate buildings, one for the ladies and the other for the gents, while having a common kitchen and dining hall. It is the hostel of the CS and the EEC department of engineering students of the university.
In recognition of the growing dissatisfaction and hence complaints among the inmates of the hostel regarding the menu served for dinner, the Dean of the engineering department, Dr Aparesh Sanyal, personally decided to investigate the matter. He set about collecting information about the preference of dinner among the inmates, separately from the gents and the ladies wing of the hostel.
Dr Sanyal was able to gather the following partial information :
Hostel inmates
Menu preference for dinner
Total
Egg Meal
Fish Meal
Chicken Meal
Gents
20
Ladies
64
Total
60
The Warden of the hostel was consulted, who after investigation declared that the following facts were clear :
1. Forty percent of the hostel inmates were ladies
2. One-third of the gentlemen inmates preferred an egg meal for dinner
3. Half the hostel inmates preferred either fish meal or chicken meal
Question:
What proportion of the lady hostel inmates preferred a fish meal for dinner ?
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