Question

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

$C(26,13)$

Short answer

The value of the given combination is 10400600.

Step-by-step solution

Step 1. Given information.

The given combination is $C(26,13)$.

Step 2. Determine the value of the given combination.

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

$\begin{array}{rcl}C(26,13)& =& \frac{26!}{(26-13)!13!}\\ & =& \frac{26!}{13!13!}\\ & =& \frac{26·25·24·23·22·21·20·19·18·17·16·15·14·13!}{13!\times 13·12·11·10·9·8·7·6·5·4·3·2·1}\\ & =& 1040060\end{array}$

Step 3. Conclusion.

The value of the given combination is 10400600.