Chapter 10.5, Problem 31E

To determine

To calculate:

The solution of the expression

  $C{}_8$

Answer to Problem 31E

The solution of the expression $C{}_8$ is $6435$ .

Explanation of Solution

Given information:

  $C{}_8$

Calculation:

The formula for permutation for $n$ objects taken $r$ at the time is as:

  $C{}_r=\frac{n!}{\left(n-r\right)!\cdot r!}\cdot \cdot \cdot \left(1\right)$

Where,

  $\begin{array}{l}n=15\\ r=8\end{array}$

Put the values in equation (1)

  $\begin{array}{l}C{}_8=\frac{15!}{\left(15-8\right)!\cdot 8!}\\ C{}_8=\frac{15!}{7!.8!}\\ C{}_8=\frac{15\times 14\times 13\times 12\times 11\times 10\times 9\times 8!}{7\times 6\times 5\times 4\times 3\times 2\times 1\times 8!}\\ C{}_8=\frac{15\times 14\times 13\times 12\times 11\times 10\times 9}{7\times 6\times 5\times 4\times 3\times 2\times 1}\\ C{}_8=6435\end{array}$

Hence, the solution of the expression $C{}_8$ is $6435$ .