Question

the principal would like to assemble a committee of 15 students from the 17 - member student council. how many different committees can be chosen? answer attempt 1 out of 2

Explanation:

Step1: Identify the problem type

This is a combination problem where we need to choose 15 students from 17, which can be solved using the combination formula \( C(n, k)=\frac{n!}{k!(n - k)!} \), where \( n = 17 \) and \( k=15 \). We can also use the property \( C(n,k)=C(n,n - k) \), so \( C(17,15)=C(17,2) \).

Step2: Calculate \( C(17,2) \)

Using the formula \( C(n,k)=\frac{n(n - 1)}{2} \) for \( k = 2 \), we substitute \( n = 17 \):
\( C(17,2)=\frac{17\times(17 - 1)}{2}=\frac{17\times16}{2} \)
First, calculate \( 17\times16 = 272 \), then divide by 2: \( \frac{272}{2}=136 \).

Answer:

136