Question

jacky hires 5 out of 10 people to build a garden. how many possible combinations of workers could she choose? 252 3,003 30,240 50

Explanation:

Step1: Recall combination formula

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

Step3: Simplify the expression

$\frac{10\times9\times8\times7\times6}{5\times4\times3\times2\times1}=\frac{10}{5}\times\frac{9}{3}\times\frac{8}{4}\times7\times\frac{6}{2}=2\times3\times2\times7\times3 = 252$.

Answer:

252