Chapter 13.1, Problem 35E

To determine

To calculate: The value of expression $C\left(9,9\right)$ .

Answer to Problem 35E

The value of expression $C\left(9,9\right)$ is $1$ .

Explanation of Solution

Given information:

The expression $C\left(9,9\right)$ .

Formula used:

If there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Calculation:

Consider the expression $C\left(9,9\right)$ .

Recall that if there are n objects taken r at a time then combination is defined as $C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$ .

Here n is 9 and r is 9.

  $\begin{array}{c}C\left(9,9\right)=\frac{9!}{9!\left(9-9\right)!}\\ =\frac{1}{0!}\\ =\frac{1}{1}\\ =1\end{array}$

Thus, the value of expression $C\left(9,9\right)$ is $1$ .