Chapter 10.5, Problem 26E

To determine

To calculate:

The solution of the expression

  $C{}_5$

Answer to Problem 26E

The solution of the expression $C{}_5$ is $56$ .

Explanation of Solution

Given information:

  $C{}_5$

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,

  $\begin{array}{l}n=8\\ r=5\end{array}$

Put the values in equation (1)

  $\begin{array}{l}C{}_5=\frac{8!}{\left(8-5\right)!\cdot 5!}\\ C{}_5=\frac{8!}{3!.5!}\\ C{}_5=\frac{8\times 7\times 6\times 5!}{3\times 2\times 1\times 5!}\\ C{}_5=\frac{8\times 7\times 6}{3\times 2\times 1}\\ C{}_5=56\end{array}$

Hence, the solution of the expression $C{}_5$ is $56$ .