Question

Compute the value of the given expression.

$7.C\left(11,5\right)$

Short answer

The answer is$462.$

Step-by-step solution

Step 1. Given information.

$C\left(11,5\right)$is given.

Step 2. Calculation.

$$\begin{gathered} C\left(11,5\right)=\frac{11!}{6!5!} \\ =\frac{11\times 10\times 9\times 8\times 7\times 6!}{6!5!} \\ =\frac{11\times 10\times 9\times 8\times 7}{5\times 4\times 3\times 2\times 1} \\ =462. \end{gathered}$$