Question

question evaluate the following combination. (6 2) select the correct answer below: 5 21 4 15 56

Explanation:

Step1: Recall combination formula

The combination formula is $C(n,k)=\frac{n!}{k!(n - k)!}$, where $n = 6$ and $k=2$.

Step2: Calculate factorial values

$n!=6!=6\times5\times4\times3\times2\times1 = 720$, $k!=2!=2\times1=2$, and $(n - k)!=(6 - 2)!=4!=4\times3\times2\times1 = 24$.

Step3: Substitute values into formula

$C(6,2)=\frac{6!}{2!(6 - 2)!}=\frac{6\times5\times4!}{2\times1\times4!}$.

Step4: Simplify the expression

Cancel out the $4!$ terms, we get $\frac{6\times5}{2\times1}=\frac{30}{2}=15$.

Answer:

15