Chapter 12.5, Problem 16AYU

To determine

To find: The value of $\left(\begin{array}{c}37\\ 19\end{array}\right)$.

Answer to Problem 16AYU

Solution:

$\left(\begin{array}{c}37\\ 19\end{array}\right) = 17672631900$

Explanation of Solution

Given:

Expression is given as $\left(\begin{array}{c}37\\ 19\end{array}\right)$.

Formula used:

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

$\begin{array}{l}\left(\begin{array}{c}n\\ j\end{array}\right) = \frac{n!}{j!\left(n - j\right)!}\\ \left(\begin{array}{c}37\\ 19\end{array}\right) = \frac{n!}{j!\left(n - j\right)!} = \frac{37!}{19!\left(37 - 19\right)!} = \frac{37!}{19! \times 18!} = 17672631900\end{array}$