AAA www-awn.aleks.comBb Week 7 - MAT300457VA016-1212-001A ALEKS - Shasia Gibbs - LearnO PROBABILITYPermutations, combination...A committee consisting of 2 faculty members and 5 students is to beformed. Every committee position has the same duties and votingrights. There are 9 faculty members and 10 students eligible to serve onthe committee. In how many ways can the committee be formed?(If necessary, consult a list of formulas.)ExplanationCheck© 2021 McGraw-Hill Education. All Rights Reservea. Terms or use Privacy I ACcessIDiity

Answered: A committee consisting of 2 faculty…

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AA
A www-awn.aleks.com
Bb Week 7 - MAT300457VA016-1212-001
A ALEKS - Shasia Gibbs - Learn
O PROBABILITY
Permutations, combination...
A committee consisting of 2 faculty members and 5 students is to be
formed. Every committee position has the same duties and voting
rights. There are 9 faculty members and 10 students eligible to serve on
the committee. In how many ways can the committee be formed?
(If necessary, consult a list of formulas.)
Explanation
Check
© 2021 McGraw-Hill Education. All Rights Reservea. Terms or use Privacy I ACcessIDiity

Expert Solution

Step 1

Given Information:

A committee consisting of 2 faculty members and 5 students is to be formed.

There are 9 faculty members and 10 students eligible to serve on the committee.

We are asked to find in how many ways the committee can be formed:

The order in which the members are selected does not matter, because each position will have the same duties and voting rights. So, we use Combinations.

Formula:

${}^{n}C_{r} = \frac{n!}{r! (n - r)!}$

Number of ways of selecting 2 faculty members from a total of 9 members is done in ${}^{9}C_{2}$ ways.

That is: ${}^{9}C_{2} = \frac{9!}{2! (9 - 2)!} = \frac{9 \times 8 \times 7!}{2 \times 1 \times 7!} = \frac{72}{2} = 36$

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