Thread: Arrangements and committees.

A company has 50 female employees, 10 of whom are in management positions, and 90 male employees, 30 of whom are in management positions. How many ways are there to choose a committee consisting of 4 women and 5 men if
(a) There must be at least one person of management rank?
(b) There must be at least one person of management rank of each sex?

(a choose b) = (a b)

I think I got this one:
(a)[(10 1)*(49 3)*(90 5)] + [(50 4)*(30 1)*(89 4)]
(b)[(10 1)*(49 3)*(30 1)*(89 4)]