Chapter 12.5, Problem 3AYU

True or False $\left(\begin{array}{l}n\\ j\end{array}\right)=\frac{j!}{\left(n-j\right)!n!}$

To determine

Check whether the given statement is true or false.

Answer to Problem 3AYU

Solution:

It is a false statement.

Explanation of Solution

Given:

Statement says that the formula for $\left(\begin{array}{c}n\\ j\end{array}\right)$ is $\left(\begin{array}{c}n\\ j\end{array}\right) = \frac{j!}{n!\left(n - j\right)!}$

Calculation:

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

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

Hence the statement is false.