Question

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

$C(18,9)$

Short answer

The value of the given combination is 48620.

Step-by-step solution

Step 1. Given information.

The given combination is $C(18,9)$.

Step 2. Determine the value of the given combination.

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

$\begin{array}{rcl}C(18,9)& =& \frac{18!}{(18-9)!9!}\\ & =& \frac{18!}{9!9!}\\ & =& \frac{18·17·16·15·14·13·12·11·10·9!}{9·8·7·6·5·4·3·2·1·9!}\\ & =& 48620\end{array}$

Step 3. Conclusion.

The value of the given combination is 48620.