Chapter 12.5, Problem 7AYU

To determine

To find: The value of $\left(\begin{array}{c}7\\ 5\end{array}\right)$.

Answer to Problem 7AYU

Solution:

$\left(\begin{array}{c}7\\ 5\end{array}\right) = 21$

Explanation of Solution

Given:

Expression is given as $\left(\begin{array}{c}7\\ 5\end{array}\right)$.

Formula used:

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

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

$\left(\begin{array}{c}7\\ 3\end{array}\right) = \frac{n!}{j!\left(n - j\right)!} = \frac{7!}{5!\left(7 - 5\right)!} = \frac{6 \times 7}{1 \times 2} = 21$