Question

Use the formula$C(n,r)=\frac{n!}{(n-r)!r!}$ to find the value of each combination.

$C(8,2)$

Short answer

The value of the given combination is 28.

Step-by-step solution

Step 1. Given information.

The given combination is $C(8,2)$.

Step 2. Determine the value of the given combination.

Using the formula, the given combination can be written as:

$\begin{array}{rcl}C(8,2)& =& \frac{8!}{(8-2)!2!}\\ & =& \frac{8!}{6!2!}\\ & =& \frac{8\times 7\times 6!}{6!\times 2\times 1}\\ & =& 28\end{array}$

Step 3. Conclusion.

The value of the given combination is 28.