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Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193

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Section
BuyFindarrow_forward

Discrete Mathematics With Applicat...

5th Edition
EPP + 1 other
ISBN: 9781337694193
Textbook Problem
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A student council consists of three freshmen, four sophomores, four juniors, and five seniors. How many committees of eight members of the council contain at least one member from each class?

To determine

To find how many committees of eight members of the council contain at least one member from each class.

Explanation

Given information:

Consider a student council consists of three freshmen, four sophomores, four juniors and live seniors.

Concept used:

Consider a student council consists of three freshmen, four sophomores, four juniors and five seniors.

The objective is to find number of committees or eight members can be formed from the above council such that the committee should contain at least one member from each class.

The number or ways to choose a subset of r elements from a set of n elements is given as follows:

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

The other notation is as follows:

C(n,r)=(nr)

Calculation:

Since the committee must contain at least one member from each class, first choose one member from each class in the following way:

One member from three freshmen can be selected in (31) ways.

One member from four sophomores can be selected in (41) ways.

One member from four juniors can be selected in (41) ways.

One member from five seniors can be selected in (51) ways

Hence, the first four members of the committee can be chosen in (31)(41)(41)(51) ways.

That is,

( 3 1)( 4 1)( 4 1)( 5 1)=[3!1!( 31)!][

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