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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

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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Chapter 14 Solutions

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Sect-14.1 P-11ESect-14.1 P-12ESect-14.1 P-13ESect-14.1 P-14ESect-14.1 P-15ESect-14.1 P-16ESect-14.1 P-17ESect-14.1 P-18ESect-14.1 P-19ESect-14.1 P-20ESect-14.1 P-21ESect-14.1 P-22ESect-14.1 P-23ESect-14.1 P-24ESect-14.1 P-25ESect-14.1 P-26ESect-14.1 P-27ESect-14.1 P-28ESect-14.1 P-29ESect-14.1 P-30ESect-14.1 P-31ESect-14.1 P-32ESect-14.1 P-33ESect-14.1 P-34ESect-14.1 P-35ESect-14.1 P-36ESect-14.1 P-37ESect-14.1 P-38ESect-14.1 P-39ESect-14.1 P-40ESect-14.1 P-41ESect-14.1 P-42ESect-14.1 P-43ESect-14.1 P-44ESect-14.1 P-45ESect-14.1 P-46ESect-14.1 P-47ESect-14.1 P-48ESect-14.1 P-49ESect-14.1 P-50ESect-14.1 P-51ESect-14.1 P-52ESect-14.1 P-53ESect-14.1 P-54ESect-14.1 P-55ESect-14.1 P-56ESect-14.1 P-57ESect-14.1 P-58ESect-14.1 P-59ESect-14.1 P-60ESect-14.1 P-61ESect-14.1 P-62ESect-14.1 P-63ESect-14.1 P-64ESect-14.1 P-65ESect-14.1 P-66ESect-14.1 P-67ESect-14.1 P-68ESect-14.1 P-69ESect-14.1 P-70ESect-14.1 P-71ESect-14.1 P-72ESect-14.1 P-73ESect-14.1 P-74ESect-14.1 P-75ESect-14.1 P-76ESect-14.1 P-77ESect-14.1 P-78ESect-14.1 P-79ESect-14.1 P-80ESect-14.1 P-81ESect-14.1 P-82ESect-14.1 P-83ESect-14.1 P-84ESect-14.1 P-85ESect-14.1 P-86ESect-14.1 P-87ESect-14.1 P-88ESect-14.1 P-89ESect-14.1 P-90ESect-14.1 P-91ESect-14.1 P-92ESect-14.1 P-93ESect-14.1 P-94ESect-14.2 P-1ESect-14.2 P-2ESect-14.2 P-3ESect-14.2 P-4ESect-14.2 P-5ESect-14.2 P-6ESect-14.2 P-7ESect-14.2 P-8ESect-14.2 P-9ESect-14.2 P-10ESect-14.2 P-11ESect-14.2 P-12ESect-14.2 P-13ESect-14.2 P-14ESect-14.2 P-15ESect-14.2 P-16ESect-14.2 P-17ESect-14.2 P-18ESect-14.2 P-19ESect-14.2 P-20ESect-14.2 P-21ESect-14.2 P-22ESect-14.2 P-23ESect-14.2 P-24ESect-14.2 P-25ESect-14.2 P-26ESect-14.2 P-27ESect-14.2 P-28ESect-14.2 P-29ESect-14.2 P-30ESect-14.2 P-31ESect-14.2 P-32ESect-14.2 P-33ESect-14.2 P-34ESect-14.2 P-35ESect-14.2 P-36ESect-14.2 P-37ESect-14.2 P-38ESect-14.2 P-39ESect-14.2 P-40ESect-14.2 P-41ESect-14.2 P-42ESect-14.2 P-43ESect-14.2 P-44ESect-14.2 P-45ESect-14.2 P-46ESect-14.2 P-47ESect-14.2 P-48ESect-14.2 P-49ESect-14.2 P-50ESect-14.2 P-51ESect-14.2 P-52ESect-14.2 P-53ESect-14.2 P-54ESect-14.2 P-55ESect-14.2 P-56ESect-14.2 P-57ESect-14.2 P-58ESect-14.2 P-59ESect-14.2 P-60ESect-14.2 P-61ESect-14.2 P-62ESect-14.2 P-63ESect-14.2 P-64ESect-14.2 P-65ESect-14.2 P-66ESect-14.2 P-67ESect-14.2 P-68ESect-14.3 P-1ESect-14.3 P-2ESect-14.3 P-3ESect-14.3 P-4ESect-14.3 P-5ESect-14.3 P-6ESect-14.3 P-7ESect-14.3 P-8ESect-14.3 P-9ESect-14.3 P-10ESect-14.3 P-11ESect-14.3 P-12ESect-14.3 P-13ESect-14.3 P-14ESect-14.3 P-15ESect-14.3 P-16ESect-14.3 P-17ESect-14.3 P-18ESect-14.3 P-19ESect-14.3 P-20ESect-14.3 P-21ESect-14.3 P-22ESect-14.3 P-23ESect-14.3 P-24ESect-14.3 P-25ESect-14.3 P-26ESect-14.3 P-27ESect-14.3 P-28ESect-14.3 P-29ESect-14.3 P-30ESect-14.3 P-31ESect-14.3 P-32ESect-14.3 P-33ESect-14.3 P-34ESect-14.3 P-35ESect-14.3 P-36ESect-14.3 P-37ESect-14.3 P-38ESect-14.3 P-39ESect-14.3 P-40ESect-14.3 P-41ESect-14.3 P-42ESect-14.3 P-43ESect-14.4 P-1ESect-14.4 P-2ESect-14.4 P-3ESect-14.4 P-4ESect-14.4 P-5ESect-14.4 P-6ESect-14.4 P-7ESect-14.4 P-8ESect-14.4 P-9ESect-14.4 P-10ESect-14.4 P-11ESect-14.4 P-12ESect-14.4 P-13ESect-14.4 P-14ESect-14.4 P-15ESect-14.4 P-16ESect-14.4 P-17ESect-14.4 P-18ESect-14.4 P-19ESect-14.4 P-20ESect-14.4 P-21ESect-14.4 P-22ESect-14.4 P-23ESect-14.4 P-24ESect-14.4 P-25ESect-14.4 P-26ESect-14.4 P-27ESect-14.4 P-28ESect-14.4 P-29ESect-14.4 P-30ESect-14.4 P-31ESect-14.CR P-1CCSect-14.CR P-2CCSect-14.CR P-3CCSect-14.CR P-4CCSect-14.CR P-5CCSect-14.CR P-6CCSect-14.CR P-7CCSect-14.CR P-8CCSect-14.CR P-9CCSect-14.CR P-1ESect-14.CR P-2ESect-14.CR P-3ESect-14.CR P-4ESect-14.CR P-5ESect-14.CR P-6ESect-14.CR P-7ESect-14.CR P-8ESect-14.CR P-9ESect-14.CR P-10ESect-14.CR P-11ESect-14.CR P-12ESect-14.CR P-13ESect-14.CR P-14ESect-14.CR P-15ESect-14.CR P-16ESect-14.CR P-17ESect-14.CR P-18ESect-14.CR P-19ESect-14.CR P-20ESect-14.CR P-21ESect-14.CR P-22ESect-14.CR P-23ESect-14.CR P-24ESect-14.CR P-25ESect-14.CR P-26ESect-14.CR P-27ESect-14.CR P-28ESect-14.CR P-29ESect-14.CR P-30ESect-14.CR P-31ESect-14.CR P-32ESect-14.CR P-33ESect-14.CR P-34ESect-14.CR P-35ESect-14.CR P-36ESect-14.CR P-37ESect-14.CR P-38ESect-14.CR P-39ESect-14.CR P-40ESect-14.CR P-41ESect-14.CR P-42ESect-14.CR P-43ESect-14.CR P-44ESect-14.CR P-45ESect-14.CR P-46ESect-14.CR P-47ESect-14.CR P-48ESect-14.CR P-49ESect-14.CR P-50ESect-14.CT P-1CTSect-14.CT P-2CTSect-14.CT P-3CTSect-14.CT P-4CTSect-14.CT P-5CTSect-14.CT P-6CTSect-14.CT P-7CTSect-14.CT P-8CTSect-14.CT P-9CTSect-14.CT P-10CTSect-14.CT P-11CTSect-14.CT P-12CTSect-14.CT P-13CTSect-14.CT P-14CTSect-14.CT P-15CTSect-14.FOM P-1PSect-14.FOM P-2PSect-14.FOM P-3PSect-14.FOM P-5PSect-14.FOM P-6PSect-14.FOM P-7P