Question

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

Short answer

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

Step-by-step solution

Step 1. Explanation

The $\left(\begin{array}{c}n\\ j\end{array}\right)$can be written as $\frac{n!}{j!\left(n-j\right)!}$

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

So, given condition is false.