Permutation, Combination & Probability — Practice

Question 1

From 7 men and 4 women, a committee of 3 with exactly 1 woman can be formed in:
(a) 84  (b) 70  (c) 120  (d) 56

Accepted Answer

1 woman (⁴C₁=4) × 2 men (⁷C₂=21) = 84.

Answer: (a) 84.

Question 2

The number of arrangements of the letters of 'LEVEL' is:
(a) 60  (b) 30  (c) 120  (d) 24

Accepted Answer

5 letters, L×2, E×2 ⇒ 5!/(2!2!) = 120/4 = 30.

Answer: (b) 30.

Question 3

From 4 red and 3 green balls, 3 are chosen with at least 2 red. Number of ways:
(a) 18  (b) 22  (c) 25  (d) 20

Accepted Answer

(2R1G) + (3R) = ⁴C₂·³C₁ + ⁴C₃ = 18 + 4 = 22.

Answer: (b) 22.

Question 4

A bag has 5 red and 4 blue balls. Two are drawn at random. P(both red)?
(a) 5/18  (b) 1/6  (c) 2/9  (d) 5/9

Accepted Answer

⁵C₂ / ⁹C₂ = 10/36 = 5/18.

Answer: (a) 5/18.

Question 5

Probability of at least one head in 3 tosses of a fair coin:
(a) 1/8  (b) 3/8  (c) 7/8  (d) 1/2

Accepted Answer

1 − P(no head) = 1 − (1/2)³ = 7/8.

Answer: (c) 7/8.

Question 6

In how many ways can 5 people sit around a circular table?
(a) 120  (b) 24  (c) 60  (d) 25

Accepted Answer

(5−1)! = 4! = 24.

Answer: (b) 24.

Practice — Permutation, Combination & Probability