Our club has 20 members, 10 boys and 10 girls. In how many ways can we choose a president and a vice-president if they must be of the same gender? Assume no one can hold both offices.
I think it is 2 of the 10 boys OR 2 of the ten girls, and order counts so that is
10*9 + 10*9 = 180
or
10P2 + 10P2 = 180
We could choose 2 of 10 boys and the same wth the girls....so we have
[C(10,2)]^2 = 2025 ways
