Permutation and Combination Practice Questions for CAT 2026 — Complete Set with Solutions
- Jul 22, 2025
- 5 min read
Updated: Apr 12
PERMUTAION AND COMBINATION Question for CAT
Q.1 In an examination, there are three multiple choice questions and each question has 4 choices. Find the number of ways in which a student can fail to answer all the questions correctly.
a.33
b.34-1
c.43-1
d.None of the above
Q.2 How many signposts can be made using 6 different coloured symbols when any number of them can be posted at a time?
a.1956
b.6!
c.66
d.None of the above
Q.3 In how many ways can you form a dancing couple from 3 boys and 3 girls so that no boy dances with his respective girlfriend?
a.2
b.6
c.0
d.None of the above
Q.4 A teacher takes 3 children from her class to the zoo at a time as often as she can, but she doesn’t take the same set of three children more than once. She finds out that she goes to the zoo 84 times more than a child goes to the zoo, Find the total number of students in her class.
a.8
b.9
c.10
d.11
Q.5 A train is going from Mumbai to Pune and make 5 stops on the way. Three persons enter the train after it has started from Mumbai with 3 different tickets. How many different sets of tickets may they have had?
a.15P3
b.3 × 15P3
c.15C3
d.None of the above
Q.6 Shakuni Mama rolls a dice 4 times. In how many outcomes will each subsequent throw be greater that the previous one?
a.15
b.48
c.30
d.60
Q.7 A die is rolled three times. Find the number of ways that the sum of the results is 11.
a.11
b.18
c.27
d.None of the above
Q.8 Shivam rolls a dice four times. In how many outcomes do we have two throws have the same number and the other two something different?
a.720
b.480
c.360
d.350
Q.9 If four-letter words (need not be meaningful ) are to be formed using the letters from the word “MEDITERRANEAN” such that the first letter is E and the fourth letter is R, then the total number of all such words is:
a.43
b.45
c.56
d.59
Q.10 If we listed all numbers from 100 to 10,000, how many times would the digit 3 be printed?
a.3980
b.3700
c.3840
d.3780
Q.11 Out of 13 objects, 4 are indistinguishable and rest are distinct. The number of ways we can choose 4 objects out of 13 objects is ............... .
a.256
b.4!
c.13! / 4!
d.None of the above
Q.12 Let Tn denote the number of triangles which can be formed using the vertices of a regular polygon of n sides. If Tn+1 – Tn = 21, then n equals:
a.6
b.7
c.8
d.9
Q.13 The number of positive numbers of not more than 10 digits formed by using 0, 1, 2 and 3 is:
a.18
b.24
c.410-310
d.410- 1
Q.14 If a small boy is asked to pick up at least one and at most n toys from (2n + 1) distinct toys and the total number of distinct selections is 255, then n is:
a.9
b.4
c.11
d.8
Q.15 There are 21 balls which are either white or black and the balls of the same colour are alike. If the number of arrangements of these balls in a row be maximum then the number of white balls can be
a.10
b.12
c.14
d.21
Q.16 Find the number of ways in which 8 identical balls can be distributed among 12 distinct boxes, if only 1 ball can go into a box.
a.128
b.12C8
c.812
d.12P8
Q.17 An entomologist noticed 15 ants crawling on his table. Exactly 13 of them were male and 2 were female. He noticed that they were crawling on the table in a random order such that no three of them were ever in the same straight line. Suddenly, three of the male ants start following one of the female ants such that, all four of them were in a single line. Then the maximum number of distinct straight lines that the entomologist can draw passing through any two ants is
a.56
b.44
c.105
d.100
Q.18 How many whole number solutions are possible for the equation x + y + z = 30 such that x < y < z?
a.496
b.75
c.450
d.None of the above
Q.19 In how many ways can three teams having 2, 2 and 3 members respectively be formed out of 7 players?
a.35
b.210
c.105
d.None of the above
Q.20 What is the sum of all 5 digit numbers which can be formed with digits 0, 1, 2, 3, 4 without repetition
a.2599980
b.2679980
c.2544980
d.2609980
Answer for Permutation and Combination for CAT
Frequently Asked Questions — Permutation and Combination Complete Practice for CAT 2026
What is the most efficient strategy for P&C questions in CAT?
Step 1: Identify the type (arrangement vs selection, linear vs circular, with/without repetition). Step 2: Handle constraints first. Step 3: Apply the formula. Step 4: Verify with small cases. Most CAT P&C questions are solved in under 3 minutes.
How many total P&C questions appear in CAT each year?
CAT typically has 3-5 P&C questions in the QA section. Topics rotate: derangements, circular arrangements, word problems, committee selection, and figure-based problems. Mastering all sub-topics gives 5-6% of total QA marks.
What are the hardest P&C concepts tested in CAT?
The hardest topics are: (1) Derangements combined with probability, (2) Circular arrangements with multiple constraints, (3) Distribution problems with identical objects, (4) Counting regions in geometric figures, (5) Number-based P&C with divisibility constraints.
How do I avoid over-counting in complex P&C problems?
The main causes of over-counting: (1) Treating identical objects as distinct, (2) Not dividing by arrangement count for identical groups, (3) Double-counting in cases that overlap. Always ask: have I counted each valid arrangement exactly once?
What is the connection between P&C and probability in CAT?
Probability = favourable outcomes / total outcomes. Many CAT probability questions reduce to counting P&C outcomes. The denominator is usually a simple permutation or combination (total arrangements), and the numerator requires constrained counting.
How do I decide between using the direct method vs complement method?
Use complement when the condition is easier to state as its opposite. Example: 'at least 1 defective' = 1 - P(no defective). Use direct when counting the favourable cases directly has fewer or simpler sub-cases.
What are the key formulas every CAT aspirant must memorise for P&C?
Essential formulas: nPr = n!/(n-r)!, nCr = n!/(r!(n-r)!), circular = (n-1)!, necklace = (n-1)!/2, derangement D(n) ≈ n!/e, stars-and-bars C(n+r-1,r-1), diagonals = n(n-3)/2, triangles from n points = C(n,3).
How should I schedule P&C preparation for CAT 2026?
Week 1: Basic counting, permutations, combinations. Week 2: Circular P&C, derangements. Week 3: Constrained problems (committee, word, number). Week 4: Figure-based, mixed problems, timed mock tests. Revise formulas daily.
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