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?

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.