A committee consists of ten women and eight men Three commit

A committee consists of ten women and eight men. Three committee members will be chosen as officers. a) How many different choices are possible? b) How many different choices are possible if all the officers are to be women? c) How many different choices are possible if all the officers are to be men? d) What is the probability that all the officers are women?

Solution

a) This is just a problem of assigning labels to 18 people: 3 are “ON” and 15 are “OFF.” There are:

18!/(3!15!)=816 ways to make the committee.

b) This is a problem just among the women: 10 people to be labeled. There are 10!/3!7!=120 committees.

c) This is a problem just among the men: 8 people to be labeled. There are 8!/3!5!= 56 committees.

d) Probability of selection being women is 3/10=0.3