a blood bank needs 5 people to help with a blood drive. 10 people have volunteered. find how many different…

Explanation:

Step1: Identify 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 $n = 10$ and $r=5$.

Step2: Calculate factorial values

$n!=10!=10\times9\times8\times7\times6\times5\times4\times3\times2\times1$, $r!=5!=5\times4\times3\times2\times1$, and $(n - r)!=(10 - 5)!=5!=5\times4\times3\times2\times1$.

Step3: Substitute values into formula

$C(10,5)=\frac{10!}{5!(10 - 5)!}=\frac{10\times9\times8\times7\times6\times5!}{5!\times5!}=\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}$.

Step4: Simplify the expression

$\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=252$.

Answer:

252