A committee must be formed from a group of 6 women and 6 men. If 3 people are selected at random, find the denominator of the probability, in simplest form, that exactly 2 women and 1 man are selected.

ATQ, Total women = 6 Total men = 6 Total people = 6 + 6 = 12 Total members to be selected = 3 Total ways to select 3 members from 12 = 12C3 12C3 = (12 × 11 × 10)/(3 × 2 × 1) = 220 Now, we need exactly 2 women and 1 man. Ways to select 2 women from 6 = 6C2 = (6 × 5)/(2 × 1) = 15 Ways to select 1 man from 6 = 6C1 = 6 Favourable ways = 15 × 6 = 90 Probability = Favourable ways/Total ways = 90/220 Now simplify 90/220: Divide numerator and denominator by 10: 90/220 = 9/22 So, the probability in simplest form is 9/22. The denominator is 22.