Question

question evaluate the following combination. (12 9) select the correct answer below: 36 1001 715 3003 220

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 12$ and $k=9$. Note that $C(n,k)=C(n,n - k)$, so $C(12,9)=C(12,12 - 9)=C(12,3)$.

Step2: Calculate factorials

$n!=n\times(n - 1)\times\cdots\times1$. So $12! = 12\times11\times10\times9!$, and $C(12,3)=\frac{12!}{3!(12 - 3)!}=\frac{12!}{3!9!}=\frac{12\times11\times10\times9!}{3\times2\times1\times9!}$.

Step3: Simplify the expression

Cancel out the $9!$ terms. Then $\frac{12\times11\times10}{3\times2\times1}=\frac{1320}{6}=220$.

Answer:

220