Chapter 10.5, Problem 30E

To determine

To calculate:

The solution of the expression

  $C{}_4$

Answer to Problem 30E

The solution of the expression $C{}_4$ is $330$ .

Explanation of Solution

Given information:

  $C{}_4$

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,

  $\begin{array}{l}n=11\\ r=4\end{array}$

Put the values in equation (1)

  $\begin{array}{l}C{}_4=\frac{11!}{\left(11-4\right)!\cdot 4!}\\ C{}_4=\frac{11!}{7!.4!}\\ C{}_4=\frac{11\times 10\times 9\times 8\times 7!}{7!\times 4\times 3\times 2\times 1}\\ C{}_4=\frac{11\times 10\times 9\times 8}{4\times 3\times 2\times 1}\\ C{}_4=330\end{array}$

Hence, the solution of the expression $C{}_4$ is $330$ .