Permutation and Combination Questions for CAT 2026 — Basic Counting Principles with Solutions
- Jul 22, 2025
- 4 min read
Updated: Apr 12
PERMUTAION AND COMBINATION Question for CAT
Q.1 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that Repetition of the digits is allowed?
a.125
b.243
c.60
d.None of the above
Q.2 How many 3-digit numbers can be formed from the digits 1, 2, 3, 4 and 5 assuming that Repetition of the digits is not allowed?
a.125
b.243
c.60
d.None of the above
Q.3 How many 3-digits even numbers can be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be repeated?
a.75
b.60
c.108
d.None of the above
Q.4 How many 4-letter code can be formed using the first 10 letters of the English alphabet, if no letter can be repeated?
a.10000
b.5040
c.256
d.None of the above
Q.5 How many 5-digit telephone numbers can be constructed using the digits 0 to 9 if each number starts with 67 and no digit appears more than once?
a.720
b.504
c.336
d.None of the above
Q.6 A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
a.9
b.8
c.6
d.None of the above
Q.7 Given 5 flags of different colours, how many different signals can be generated if each signal requires the use of 2 flags, one below the other?
a.20
b.25
c.120
d.None of the above
Q.8 How many 4-digit numbers are there with no digit repeated?
a.3024
b.5040
c.4536
d.None of the above
Q.9 From a committee of 8 persons, in how many ways can we choose a chairman and a vice chairman assuming one person cannot hold more than one position?
a.56
b.64
c.8!
d.None of the above
Q.10 There are 5 different buses running from Indore to Mumbai and vice versa. In how many ways can a person travel from Indore to Mumbai and return from Mumbai to Indore?
a.10
b.20
c.25
d.None of the above
Q.11 There are 5 different buses running from Indore to Mumbai and vice versa. In how many ways can a person travel from Indore to Mumbai and return by a different service?
a.10
b.20
c.25
d.None of the above
Q.12 In how many ways can 4 people be seated on 5 different chairs?
a.120
b.45
c.54
d.30
Q.13 In how many ways can 4 people vacate an elevator (order not important) if there are 5 floors in the building?
a.120
b.45
c.54
d.30
Q.14 In how many ways can 5 monkeys be divided among 4 masters, such that each monkey can have only one master but any master can have any number of monkeys?
a.120
b.45
c.54
d.30
Q.15 In how many ways can 3 different rings be worn on 5 fingers?
a.210
b.120
c.125
d.None of the above
Answer for Permutation and Combination for CAT
1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
A | C | C | B | C | B | A | C | A | C |
11 | 12 | 13 | 14 | 15 | |||||
B | A | C | B | A |
Frequently Asked Questions — Basic Counting Principles for CAT 2026
What are the fundamental counting principles?
Two core principles: (1) Rule of Product (AND rule): if event A can occur in m ways and event B in n ways, both together occur in m x n ways. (2) Rule of Sum (OR rule): if A can occur in m ways OR B in n ways (mutually exclusive), total = m + n ways.
What is the difference between permutation and combination?
Permutation counts ordered arrangements: nPr = n!/(n-r)!. Combination counts unordered selections: nCr = n!/[r!(n-r)!]. Key question: does order matter? If yes, use permutation; if no, use combination.
What is Pascal's identity and why is it useful?
Pascal's identity: C(n,r) = C(n-1,r-1) + C(n-1,r). It relates combinations and forms Pascal's Triangle. In CAT, it simplifies computation: instead of calculating large factorials, use the recursive relationship.
How do I solve problems involving identical objects?
For distributing n identical objects into r distinct groups: use stars and bars: C(n+r-1, r-1). For permutations with identical objects: n!/( p! x q! x ...) where p, q, ... are counts of each repeated element.
What is the bijection principle in counting?
The bijection principle states that if two sets have a one-to-one correspondence (bijection), they have the same number of elements. This is used to solve counting problems by transforming them into simpler equivalent problems.
How do I approach 'at least' and 'at most' problems?
For 'at least k': use complement method = Total - (cases with fewer than k). For 'at most k': sum cases for 0, 1, 2, ..., k directly. The complement method is faster when 'fewer than k' cases are simpler to count.
What is the pigeonhole principle?
If n items are placed into m containers and n > m, at least one container must have more than one item. More precisely: at least one container has at least ceil(n/m) items. CAT tests this in word problems about minimum guaranteed outcomes.
How should I build speed in basic counting for CAT?
Practise the product and sum rules on small examples first. Build intuition for when order matters. Memorise nCr for small values (n up to 10, r up to 5). Solve 10 mixed problems daily for 2 weeks, focusing on whether to use P or C.
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