Question

A group of 4 will represent your interest club. If there are 3 male students and 3 female students, let Y be the RV representing the number of female students,

a.) how many possible groups are there?

Answer 1

а) There are next posiible groups(m - male, f - female): (1m,3f), (2m,2f), (3m,1f). Now we should calculate the number of ways to form each group. Since the order is not important and repetitions is not allowed, then:

$(1m,3f)={4 \choose 1}*{4 \choose 1}=16$

$(2m,2f)={4 \choose 2}*{4 \choose 2}=36$

$(3m,1f)={4 \choose 3}*{4 \choose 1}=16$

So, there are 16 + 36 + 16 = 68 possible groups