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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

Dance Committee A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. If 6 freshmen, 8 sophomores, 12 juniors, and 10 seniors are eligible to be on the committee, in how many ways can the committee be chosen?

To determine

To find:

The number of ways by which the committee is chosen.

Explanation

Given:

A school dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors. There are 6 freshmen, 8 sophomores, 12 juniors, and 10 seniors who are eligible to be on the committee.

Approach:

The consequence of the Fundamental Counting Principle is for any number of events; that is, if E1, E2, E3….. EK are events that occur in order and E1 occur in n1 ways, E2 occur in n2 ways and so on, then the events can occur in order in n1×n2×.....×nK ways.

Also,

The number of combinations of n distinct objects taken r at a time is,

C(n,r)=n!r!(nr)!;(rn)

Calculation:

The dance committee is to consist of 2 freshmen, 3 sophomores, 4 juniors, and 5 seniors.

The number of ways by which 2 freshmen is chosen from 6 freshmen is

C(6,2)=6!2!(62)!=6×5×4!2×1×4!=15

The number of ways by which 3 sophomores is chosen from 8 sophomores is

C(8,3)=8!3!(83)!=8×7×6×5!3×2×1×5!=56

The number of ways by which 4 juniors is chosen from 12 juniors is

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Chapter 14 Solutions

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