Question

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

$C(15,15)$

Short answer

The value of the given combination is 1.

Step-by-step solution

Step 1. Given information.

The given combination is $C(15,15)$.

Step 2. Determine the value of the given combination.

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

$\begin{array}{rcl}C(15,15)& =& \frac{15!}{(15-15)!15!}\\ & =& \frac{15!}{0!15!}\\ & =& \frac{15!}{1\times 15!}\\ & =& 1\end{array}$

Step 3. Conclusion.

The value of the given combination is 1.