CAT Permutations, Combinations and Sets questions with solutions
Counting arrangements and selections, including set and Venn diagram counting. 28 questions from our 2016–2025 CAT pattern papers. Each has the answer and a full solution.
CAT 2025
CAT 2024
- In how many ways can 5 boys and 3 girls be seated in a row such that no two girls sit together?
- How many distinct arrangements of the letters of the word 'ORANGE' are possible if all the vowels (O, A, E) must always come together?
- In how many ways can 5 men and 3 women be seated in a row such that no two women sit next to each other?
CAT 2023
CAT 2022
CAT 2021
- In how many ways can the letters of the word GARDEN be arranged so that the two vowels always come together?
- In how many ways can 10 identical chocolates be distributed among 4 children so that every child gets at least 1 chocolate and no child gets more…
- In how many ways can the letters of the word ORANGE be arranged so that all three vowels occupy only the odd positions (1st, 3rd and 5th)?
CAT 2020
- How many four-digit numbers with all digits distinct are divisible by 5?
- In how many distinct ways can the letters of the word COMMITTEE be arranged so that the two M's are not next to each other?
- In how many ways can the letters of the word BANANA be arranged so that no two A's are adjacent?
- In a group of 100 people, 70 read newspaper A, 60 read newspaper B and 50 read newspaper C. Every person reads at least one of the three newspapers.…
CAT 2019
- In how many ways can the letters of the word ARRANGE be arranged so that the two R's are not together?
- In a batch of 100 students, 60 study Mathematics, 50 study Physics and 40 study Chemistry. 25 study both Mathematics and Physics, 20 study both…
- In how many distinct ways can the letters of the word SYSTEM be arranged so that the two S's are not next to each other?
CAT 2018
- In how many ways can the letters of the word ELEVEN be arranged so that no two E's are next to each other?
- How many 4-letter code words (no letter repeated) can be formed using the letters of the word COMPUTER such that the word contains at least one vowel?
- In a class of 100 students, 60 study Mathematics, 50 study Physics and 45 study Chemistry. 25 study both Mathematics and Physics, 20 study both…
CAT 2017
- In how many distinct ways can the letters of the word BANANA be arranged so that the two N's are not next to each other?
- In how many distinct arrangements of the letters of the word BANANA are the two N's not next to each other?
- In a group of 100 students, 60 drink tea, 50 drink coffee and 40 drink juice. 25 drink both tea and coffee, 20 drink both coffee and juice, 15 drink…
CAT 2016
- In how many ways can 15 be written as a sum of three distinct positive integers, if the order of the terms does not matter? (For example, 1 + 2 + 12…
- In a class of 60 students, 35 like tea, 30 like coffee and 10 like neither. How many students like exactly one of the two beverages?
- In how many ways can the letters of the word BANANA be arranged so that the two N's are NOT together?
Other Quant topics
Time, Speed and Distance 38Time and Work 23Pipes and Cisterns 11Simple and Compound Interest 33Profit, Loss and Discount 42Mixtures and Alligation 35Ratio and Partnership 17Percentages 30Averages 19Probability 20Logarithms and Indices 16Quadratic Equations and Polynomials 18Linear Equations 9Inequalities and Modulus 19Functions 22Maxima and Minima 11Progressions 29Remainders and Divisibility 15Number System 19Coordinate Geometry 29Triangles 24Circles 18Polygons and Quadrilaterals 12Mensuration 13