a coach chooses six out of eight players to go to a skills workshop. if order does not matter, in how many…

Explanation:

Step1: Identify 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 $n = 8$ and $r=6$.

Step2: Calculate factorial values

We know that $n!=n\times(n - 1)\times\cdots\times1$. So $8! = 8\times7\times6\times5\times4\times3\times2\times1$, $6! = 6\times5\times4\times3\times2\times1$, and $(8 - 6)!=2!=2\times1$. Then $C(8,6)=\frac{8!}{6!(8 - 6)!}=\frac{8!}{6!2!}=\frac{8\times7\times6!}{6!\times2\times1}$.

Step3: Simplify the expression

Cancel out the $6!$ terms in the numerator and denominator. We get $\frac{8\times7}{2\times1}=\frac{56}{2}=28$.

Answer:

C. 28