Chapter 14.CR, Problem 23E

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4th Edition

James Stewart + 2 others

ISBN: 9781305071742

Textbook Problem

**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.

To determine

(a)

**To find:**

The number of ways a committee can be chosen with no restriction is placed on the number of men and women on the committee.

Explanation

**Approach:**

A combination of

If a set has

**Calculation:**

Substitute

To determine

(b)

**To find:**

The number of ways a committee can be chosen with exactly four men and three women.

To determine

(c)

**To find:**

The number of ways a committee if Susie refuses to serve on the committee.

To determine

(d)

**To find:**

The number of ways a committee such that at least five woman must serve on the committee.

To determine

(e)

**To find:**

The number of ways a committee such that at most two men can serve on the committee.

To determine

(f)

**To find:**

The number of ways the committee is to have a chairman, a vice chairman, a secretary and four other members.

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