Question

A group of seven women and six men must select a four-person committee.

How many committees are possible if it must consist of the following?

(a) two women and two men
(b) any mixture of men and women
(c) a majority of women

Answer 1

Given 7 women, six men.
(a) two women and two men
C(7,2)*C(6,2)
=7!/(2!5! * 6!/(2!4!)
=21*15
=315
(b) any
C(13,4)=715
(c) majority women
C(7,4)+C(7,3)*C(6,1)
=35+(35*6)
=245