Maths · Algebra · chapter 6 of 14

Class 11 Maths Chapter 6: Permutations and Combinations MCQs with answers

10 multiple-choice questions on Permutations and Combinations, each with its answer and the reason, written from the NCERT chapter. For school exams on the CBSE pattern and JEE Main, which are set from the same NCERT chapter. Open a question's solution to check your working; then take the free test to find your next chapter.

Question 1
From Pune to Mumbai there are 4 trains, and from Mumbai to Goa there are 3 buses. In how many ways can Kavya travel from Pune to Goa through Mumbai, taking one train and then one bus?
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Answer: (b) 12

A train can be chosen in 4 ways, and after it a bus in 3 ways; by the multiplication principle, 4 × 3 = 12. Adding (7) treats the two choices as alternatives, not as events in succession.

Question 2
Five different letters are to be posted, each in any one of 3 letter boxes. The number of ways of posting them is
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Answer: (c) 243

Each of the 5 letters has 3 choices of box, and a box may take any number of letters, so the count is 3 × 3 × 3 × 3 × 3 = 35 = 243. 53 gives each box a choice of letter, which is the wrong way round.

Question 3
For a natural number n, (n + 1)!(n − 1)! equals
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Answer: (d) n(n + 1)

(n + 1)! = (n + 1) × n × (n − 1)!, so the quotient is (n + 1)n = n(n + 1).

Question 4
The value of 0! + 1! + 2! + 3! is
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Answer: (b) 10

0! = 1 by definition, 1! = 1, 2! = 2, 3! = 6; the sum is 1 + 1 + 2 + 6 = 10. Taking 0! as 0 gives 9.

Question 5
Seven runners take part in a school race. In how many ways can the gold, silver and bronze medals be awarded, if no runner gets more than one medal?
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Answer: (a) 210

The medals are different, so order matters: ⁷P₃ = 7 × 6 × 5 = 210. ⁷C₃ = 35 ignores which medal goes to whom; 73 lets one runner win twice.

Question 6
The value of ¹⁵C₁₃ is
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Answer: (a) 105

¹⁵C₁₃ = ¹⁵C₂ = 15 × 142 = 105. 210 is ¹⁵P₂, the count without dividing by 2!.

Question 7
Nine players take part in a chess tournament in which every player plays every other player exactly once. The number of games played is
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Answer: (c) 36

A game is fixed by its pair of players, and the pair A, B is the same as B, A: ⁹C₂ = 9 × 82 = 36. 72 counts each game twice.

Question 8
A word has 6 letters, of which one letter appears exactly twice and the other four are all different. The number of arrangements of all its letters is
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Answer: (d) 360

By Theorem 3, n!/p! = 6!/2! = 720/2 = 360.

Question 9
Which of the following is counted by combinations, not by permutations?
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Answer: (b) Choosing 3 members of a committee from 10 people

In a committee the members have no order: the committee of X, Y, Z is the same as Z, Y, X. The other three are arrangements in which order changes the outcome.

Question 10
The value of ⁸P₀ + ⁸C₈ + 0! is
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Answer: (c) 3

ⁿP₀ = 1, ⁿCn = 1 and 0! = 1, so the sum is 1 + 1 + 1 = 3.

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