Question

A clothing manufacturer interviews 12 people for four openings in the human resources department of the company. Five of the 12 people are women. If all 12 are qualified, in how many ways can the employer fill the four positions if exactly two women are selected?

Answer 1

Number of ways to satisfy the condition: 10*21 = 210

Explanation:

Given:

Total 12 peoples and 4 openings

Including 5 women and 7 men

As the condition suggest that if the exactly two women are selected, so number of ways to select two women out of 5 is

Number of ways to pick 2 women:

5C2 = (5!)/((5-2)!*2!) = 120/12 = 10

Number of ways to pick remaining 2 men:

7C2 = (7!)/((7-2)!*2!) = 5040/240 = 21

As the condition is to select four peoples , it means

Total number of ways to satisfy the problem condition: 10*21 = 210