Hello CAT 2024 candidates, On November 24, the CAT exam 2024 for MBA admissions 2025–2027 will take place. In this CAT 2024 60 days preparation guide series of Careers360, we will discuss the strategies to prepare Permutation and Combination Questions For CAT Exam for day 35 that can help you prepare well and crack the CAT entrance test 2024.
CAT Exam Important Topic: Strategy to Prepare “Permutations and Combinations (Principle of Counting and Arrangement)” and CAT Permutation and Combination Questions.
Permutation and combination CAT Formula and Concepts:
Fundamental Principle of Counting
Rule of Product: Taking 1 out of m objects and taking 1 out of n objects, the total number of ways taking 1 out of each of m and n = m x n
Rule of Addition: Taking 1 out of m objects or taking 1 out of n objects, the total number of ways taking 1 out of each of either m or n = m + n
Linear Arrangements: Arranging n objects at n different places = n!
Circular Arrangements: Arranging n objects at n different places(circularly) = (n-1)!
Permutation and Combination Examples:
Permutation Examples:
Arranging Books: You have 4 different books (A, B, C, D) and you want to arrange them on a shelf. The number of ways to arrange them in a specific order would be a permutation. For example, ABCD, ACBD, BCAD, etc.
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Choosing a Committee: You have 5 people and you want to choose a president, vice-president, and secretary from among them. The order in which you choose these roles matters, so this is a permutation.
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Picking Fruits: You have 6 different fruits and you want to choose 3 to take with you. The order in which you choose them doesn't matter, only which fruits you select. This is a combination.
Selecting a Pizza Topping: You are ordering a pizza and can choose 4 toppings from a list of 8. The order in which the toppings are placed on the pizza doesn't matter, so this is a combination.
CAT Exam: Basic Principle of Counting: Permutation And Combination Previous Year Questions
Q1. How many four-digit numbers, which are divisible by 6, can be formed using the digits 0, 2, 3, 4, and 6, such that no digit is used more than once and 0 does not occur in the left-most position? [TITA, CAT 2017]
Solution:
This CAT Permutation and Combination questions are based on Arrangements
Some points to be noticed: permutation and combination formula -
0 does not occur in the leftmost position.
If the numbers are to be divisible by 6 it should be a multiple of 2 and 3.
So, the number should be an even number and also be divisible by 3.
Permutations and combinations Examples:
At the unit place, there can be either 0, 2, 4, 6
Permutations and combinations Case 1: Unit Place is ‘0’
Sum of the rest of three should be divisible by 3, The possible pairs are
2, 3, 4; Number of arrangements = 3! = 6.
2, 4, 6; Number of arrangements = 3! = 6.
Total Numbers in Case 1 = 12
Permutations and combinations Case 2: Unit Place is ‘2’
Sum of all four digits should be divisible by 3, The possible pairs are
0, 4, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
3, 4, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 3, 4 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 2 = 14
Permutations and combinations Case 3: Unit Place is ‘4’
Sum of all four digits should be divisible by 3, The possible pairs are
2, 3, 6 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 2, 6 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
0, 3, 2 (Sum 0+ 4+ 3+ 2= 9); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 3 = 14
Permutations and combinations Case 4: Unit Place is ‘6’
Sum of all four digits should be divisible by 3, The possible pairs are
2, 3, 4 (Sum 2+ 3 + 4+ 6 = 15); Number of arrangements = 3! = 6.
0, 2, 4 (Sum 0+ 4+ 6+ 2= 12); Left most place is filled in 2 ways and the remaining two places are filled in 2 ways, so total numbers formed = 4
Total Numbers in Case 4 = 10
Therefore, in total we can form 12 + 14 + 14 + 10 = 50 four- digit numbers.
Hence, the answer is 50
Pre-requisite to permutations and combinations for CAT exam
Vedic Maths
Factorial
CAT study material: References to Study (Theory) permutations and combinations for CAT exam
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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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