   Chapter 14.CT, Problem 8CT ### 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

# A board of directors consisting of eight members is to chosen from a pool of 30 candidates. The board is to have a chairman, a treasurer, a secretary, and five other members. In how many ways can the board of directors be chosen?

To determine

The number of ways in which a team can be selected.

Explanation

Approach:

The number of ways of selecting r objects taken at a time from a total of n objects is given by,

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

The Fundamental counting principle states that “For any number of events E1,E2,.....,En occurs in n1,n2,....,nn number of ways, then the whole event can occur in n1×n2×....×nn ways.”

The number of ways in which one photo frame of each grandchild can be selected is given by,

Numberofways=n1×n2×n3×n4 ...(2)

Given:

Number of candidates are 30.

Calculation:

There will be only one chairman amongst the candidates.

Calculate the number of ways in which one chairman can be selected.

Substitute 30 for n and 1 for r in equation (1) to find the number of ways in which chairman can be selected.

C(30,1)=30!1!(301)!=30×29!29!=30

There will be only one treasurer amongst the rest of the candidates.

Calculate the number of ways in which one treasurer can be selected.

Substitute 29 for n and 1 for r in equation (1) to find the number of ways in which a treasurer can be selected.

C(29,1)=29!1!(291)!=29×28!28!=29

There will be only one secretary amongst the rest of the candidates

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