   Chapter 14.1, Problem 77E ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742

#### Solutions

Chapter
Section ### Algebra and Trigonometry (MindTap ...

4th Edition
James Stewart + 2 others
ISBN: 9781305071742
Textbook Problem

# APPLICATIONS 7 5 - 9 0 ■ Counting Principles Solve these exercises by using the appropriate counting principle(s).Choosing a Committee A committee of six is to be chosen from a class of 20 students. The committee is to consist of a chair, a secretary and four other members. In how many different ways can the committee be picked?

To determine

To find:

The number of different ways the committee of six members can be picked.

Explanation

Given:

A committee of six is to be chosen from a class of 20 students. The committee consists of a chair, a secretary and four other members.

Approach:

The order for picking a student for the post of a chair, a secretary, and four other members is important, But the order for picking the four other members is not important.

Write the formula of the number of permutations,

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

Here, n is the total number of objects and r is the number of objects chosen.

Write the formula of the number of combinations,

C(n,r)=n!r!(nr)!(2)

Calculation:

Substitute 20 for n and 1 for r in equation (1) as.

P(20,1)=20!(201)!=20×19!19!=20(3)

Substitute 19 for n and 1 for r in equation (1)

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