Chapter 14.CR, Problem 23E

1-24 Counting These exercises involve counting.

Choosing a Committee A committee of seven is to be chosen from a group of ten men and eight women. In how many ways can the committee be chosen using each of the following selection requirements?

(a) No restriction is placed on the number of men and women on the committee.

(b) The committee must have exactly four men and three women.

(c) Susie refuses to serve on the committee.

(d) At least five women must serve on the committee.

(e) At most two men can serve on the committee.

(f) The committee is to have a chairman, a vice chairman, a secretary, and four other members.