Chapter 0.5, Problem 8E

To determine

To evaluate: the given combination.

Answer to Problem 8E

  $C{}_7=792$ .

Explanation of Solution

Given information:

  $C{}_7$

Solving the given permutation,

  $\begin{array}{c}C{}_7=\frac{12!}{7!\left(12-7\right)!}\\ =\frac{12!}{7!5!}\\ =\frac{12\times 11\times 10\times 9\times 8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{7\times 6\times 5\times 4\times 3\times 2\times 1\times 5\times 4\times 3\times 2\times 1}\\ =\frac{12\times 11\times 10\times 9\times 8}{5\times 4\times 3\times 2\times 1}\\ =792\end{array}$

So,

After evaluating,

  $C{}_7=792$ .