A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 3 women?

Question: A small company employs 3 men and 5 women. If a team of 4 employees is to be randomly selected to organize the company retreat, what is the probability that the team will have exactly 3 women?

Solution:
A small company employs 3 men and 5 women.
Total people = 8

ways of selecting 4 people from 8 = ⁸C₄
= 70

ways of selecting 3 women from 5 = ⁵C₃
ways of selecting 1 men from 3 = ³C₁

∴ probability = (⁵C₃ × ³C₁)/ 70
= (10 × 3)/70
= 3/7