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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.
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.
Part-1: Quantitative Aptitude for CAT exam (Permutation and Combination Aptitude)
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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nCr = nCn-r
Out of n given things, the number of ways of selecting any number = 2n -1.
Dividing n items into two groups of p and q items
= n!/q! p!
If p =q and two groups are not identical; a number of groups will be n! /(p!)2
If p =q and two groups are identical; a number of groups will be n!/2! (p!)2
The number of diagonals in an n-sided regular polygon = nC2 – n
Divide questions of distributions into the following categories while solving:
Identical Objects Identical Places
Identical Objects Distinct Places
Distinct Objects Identical Places
Distinct Objects Distinct Places
Learn all the formulas and understand their applications.
Practice all kinds of Permutation and Combination problems.
CAT Exam:
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]
Permutation and Combination examples with answers: 1000 ways
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
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
CAT permutation and combination questions
Vedic Maths
Factorial
Fundamental Principle of counting
CAT study material: References to Study (Theory)
Permutation and Combination problems:
NCERT Class 11 Maths
CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=509qwiX-3qY)
https://www.youtube.com/watch?v=QsKl5GbBcHU
Study material: References to Practice CAT Permutation and Combination Questions (Syllogism)
How to prepare quantitative Aptitude for CAT by Arun Sharma.
CAT Funda (YouTube, Link: https://www.youtube.com/watch?v=RAOTFT1_Ynk)
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
Set Theory
Concept of Syllogism
References to Study (Theory syllogism questions for CAT
Verbal and Non-Verbal Reasoning by B S Sijwali
CAT Handa (YouTube link: https://www.youtube.com/watch?v=4N8qsbClYpA)
References to Practice syllogism questions for CAT
Verbal and Non-Verbal Reasoning by R S Agrawal.
MBA Entrance Exams Previous years Papers.3. ELITES GRID (YouTube; Link: https://www.youtube.com/watch?v=sn_k4q6BHxk)
Part-3: CAT Exam Preparation 2025: CAT exam tips for VARC (Verbal Ability & Reading Comprehension)
CAT Exam Important Topic: Strategy to Prepare “Comparison (Comparatives and Superlatives)” for CAT-2025.
CAT Important Concepts
Comparative Adjectives and Superlative Adjectives Fast?Faster (Comparative)?Faster (Superlative)
Comparative Adverbs and Superlative Adverbs
Negative Comparatives
CAT Previous Years' Questions on Comparison (Comparatives and Superlatives).
Q1: My daughter is__________ than my wife
more taller
more tall
taller
tall
Ans: [C]
Here is a comparison between two persons.
Q2. This is the ____________chocolate I have ever had.
best
better
good
well
Ans: [A]
‘best’ is best suited because comparison is with all time.
CAT 2025:Prerequisite
Sentence Structure
Adjectives and Adverbs
Comparative and Superlative Degrees
Tips and Tricks for CAT Exam
Learn comparative and superlative adjectives.
Learn the pronunciation of these comparatives and superlatives:
long /lɒŋ/ longer /lɒŋgə(r)/ longest /lɒŋgəst/
strong /strɒŋ/ stronger /strɒŋgə(r)/ strongest /strɒŋ gəst/
young /jʌŋ/ younger /jʌŋgə(r)/ youngest /jʌŋgəst/Put structurally equivalent verbs in the same form.
Some one-syllable adjectives have irregular comparative and superlative forms:
bad, worse, worst far, farther/further, farthest/furthest
good, better, best old, older/elder, oldest/eldest
Two-syllable adjectives
Two-syllable adjectives ending in -y change y to i and take the -er and -est endings:
busy, busier, busiest
happy, happier, happiest
easy, easier, easiest
funny, funnier, funniest
Comparative adjectives: using much, a lot, far, etc.
Comparative adjectives: using than
Comparative adjectives: -er and -er, more and more
Comparative adjectives: the -er, the -er and the more …, the more …
Use than, not that or as to introduce a clause after a comparative adjective or adverb
CAT exam: References to Study (Theory)
Wren and Martin
(https://www.youtube.com/watch?v=cpQbmdKkNFs)
CAT exam: References to Study (Practice)
Verbal Ability for CAT by Arun Sharma and Meenakshi Upadhyay.
CAT Previous years Papers and Sample Papers.
(youTube; Link: https://www.youtube.com/watch?v=pm9fq1MbR_I)
Day 37 will be posted tomorrow, so practice and stay focused.
Thank you!
All the Best!
CAT 2023 Official Question Paper and Answer Key (Slot 1) | |
CAT 2023 Official Question Paper and Answer Key (Slot 3) |
CAT registration will start around August 2025. Candidates can start registering for the CAT exam on the official website of the CAT.
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.
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.
Yes, mock tests are crucial for CAT 2025 preparation since it helps the candidate, to carefully analyse their weakness and strength.
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.
Hi aspirant,
You can refer to the link attached above for more information on the same.
All the best!
Hi aspirant,
You can refer to the link given above for more information on the same.
All the best!
Hello dear,
The CAT exam requires a significant amount of time for preparation, including brushing up on basic concepts and practicing advanced problem-solving. Starting too early can feel overwhelming and may not be sustainable with other academic commitments.
The CAT exam requires a level of focus and maturity that is not always present in class 9. Starting preparation at this stage can be challenging to maintain. At class 9, you're primarily focused on learning foundational concepts. So you just need to boost your fundamentals by practicing more and more at class 9 because the Quantitative Aptitude section of CAT syllabus includes all the topics of Mathematics from Class 9 to 10 such as Arithmetic, Geometry, Algebra, Trigonometry and Mensuration.
Start Preparation 12 Months Prior:
Identify Weak Sections:
I hope you got your answer, That's all Thank you.
IIFT CAT Cutoff 2024
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Note: Final selection also includes WAT, GD, PI, academics, and work experience.
To prepare for CDS, CGL, and CAT during graduation, create a clear study schedule focusing on basics, reasoning, and aptitude. Practice daily mocks, improve time management, and stay consistent. Balance college and preparation with discipline and regular revision.
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