Question

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

$C(6,2)$

Short answer

The value of the given combination is 15.

Step-by-step solution

Step 1. Given information.

The given combination is $C(6,2)$.

Step 2. Determine the value of the given combination.

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

$\begin{array}{rcl}C(6,2)& =& \frac{6!}{(6-2)!2!}\\ & =& \frac{6!}{4!2!}\\ & =& \frac{6\times 5\times 4!}{4!\times 2\times 1}\\ & =& 15\end{array}$

Step 3. Conclusion.

The value of the given combination is 15.