Chapter 12.5, Problem 8AYU

In Problems 5-16, evaluate each expression.

$\left(\begin{array}{l}9\\ 7\end{array}\right)$

To determine

To find: The value of $\left(\begin{array}{c}9\\ 7\end{array}\right)$.

Answer to Problem 8AYU

Solution:

$\left(\begin{array}{c}9\\ 7\end{array}\right) = 36$

Explanation of Solution

Given:

Expression is given as $\left(\begin{array}{c}9\\ 7\end{array}\right)$.

Formula used:

The symbol $\left(\begin{array}{c}n\\ j\end{array}\right)$ is defined as

$\left(\begin{array}{c}n\\ j\end{array}\right) = \frac{n!}{j!\left(n - j\right)!}$

$\left(\begin{array}{c}9\\ 7\end{array}\right) = \frac{n!}{j!\left(n - j\right)!} = \frac{9!}{7!\left(9 - 7\right)!} = \frac{8 \times 9}{1 \times 2} = 36$