Question

There are 9 candidates total, 5 male and 4 female, who run for 4 committee positions. Suppose that each person is equally likely to be elected. What is the probability that 2 males and 2 females are elected?

Answer 1

Use the hypergeometric distribution.
M=number of Men=5
F=number of women=4
m=number of men elected=2
f=number ow women elected=2.

Assuming equal chance to get elected, then
P(2M,2F)=C(M,m)*C(F,f)/C(M+F,m+f)
=C(5,2)*C(4,2)/C(9,4)
=10*6/126
=10/21

Reference: Hypergeometric distribution.