Multiple choice

A group consists of 5 men and 4 women. A committee of 3 members is to be formed. If one person is selected as the head, and the other two as members, what is the probability that the committee includes at least one woman?

  1. 46 56

  2. 37 42

  3. 48 52

  4. 49 56
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The probability of selecting three men is C(5,3)/C(9,3) = 10/84 = 5/42. Therefore, the probability of including at least one woman is 1 - 5/42 = 37/42. Selecting a head does not change the committee composition probability.

AI explanation

The total number of ways to choose 3 members from 9 people is 9! / (6! × 3!) = 84. The number of committees with no women (all men) is 5! / (2! × 3!) = 10. The probability of having at least one woman is (84 - 10) / 84 = 74/84 = 37/42.

Keep practicing — related questions