Question

question 3
3 pts
a local school board of 17 people needs to form a committee of 6 people. how many different ways can this committee be formed?

Explanation:

Step1: Identify the combination formula

The formula for combinations is \(C(n,r)=\frac{n!}{r!(n - r)!}\), where \(n\) is the total number of items, and \(r\) is the number of items to be chosen. Here, \(n = 17\) and \(r=6\).

Step2: Calculate factorial values

First, calculate \(n!=17! = 17\times16\times15\times14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\), \(r!=6! = 6\times5\times4\times3\times2\times1\), and \((n - r)!=(17 - 6)!=11! = 11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1\). Then \(C(17,6)=\frac{17!}{6!(17 - 6)!}=\frac{17\times16\times15\times14\times13\times12\times11!}{6!\times11!}\).

Step3: Simplify the expression

Cancel out the \(11!\) terms. We get \(C(17,6)=\frac{17\times16\times15\times14\times13\times12}{6\times5\times4\times3\times2\times1}\).

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Answer:

\(12376\)