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Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

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BuyFindarrow_forward

Algebra and Trigonometry (MindTap ...

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 r objects from a set is any subset of the set that contains r elements (without regard to order).

If a set has n objects, then the number of combination of r elements from the set is denoted C(n,r) and is called the number of combination of n objects taken r at a time.

C(n,r)=n!r!(nr)! ……(1)

Calculation:

Substitute 18 for n and 7 for r in equation (1)

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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Chapter 14 Solutions

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