Question

how many different five - person committees can be formed in a club with 14 members?
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Explanation:

Step1: Identify the problem type

This is a combination problem where we need to find the number of ways to choose 5 people from 14, which is calculated using the combination formula \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 14 \) and \( k=5 \).

Step2: Apply the combination formula

First, calculate the factorials:

• \( n!=14! = 14\times13\times12\times11\times10\times9\times8\times7\times6\times5\times4\times3\times2\times1 \)
• \( k!=5! = 5\times4\times3\times2\times1 \)
• \( (n - k)!=(14 - 5)!=9! = 9\times8\times7\times6\times5\times4\times3\times2\times1 \)

Now, substitute into the formula:

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Answer:

2002