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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 The U.S. Senate has two senators from each of the 50 states. In how many ways can a commit-tee of five senators be chosen if no state is to have two members on the committee?

To determine

To find:

The number of ways can a committee of five senators be chosen if no state is to have two members 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 as C(n,r) and is called the number of combination of n objects taken r at a time. Then,

C(n,r)=n!r!(nr)! (1)

Calculation:

The U.S senate has two senators from each 50 states. A committee of 5 senators is to be chosen if no state is to have two members on the committee. This can be view as choosing 5 senators from 50 states which can be done in C(50,5) ways

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Chapter 14 Solutions

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