Question

evaluate the following combination: 12 c 6

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,r)=\frac{n!}{r!(n - r)!}$, where $n = 12$ and $r=6$.

Step2: Calculate factorial values

$n!=n\times(n - 1)\times\cdots\times1$. So, $12! = 12\times11\times10\times9\times8\times7\times6!$, and $(12 - 6)!=6!$. Then $C(12,6)=\frac{12!}{6!×6!}=\frac{12\times11\times10\times9\times8\times7\times6!}{6!\times6!}=\frac{12\times11\times10\times9\times8\times7}{6!}$.
Since $6!=6\times5\times4\times3\times2\times1 = 720$.

Step3: Perform the calculation

$\frac{12\times11\times10\times9\times8\times7}{720}=\frac{665280}{720}=924$.

Answer:

924