Question

Evaluate$\left(\begin{array}{c}7\\ 3\end{array}\right)$

Short answer

The value of $\left(\begin{array}{c}7\\ 3\end{array}\right)=35$

Step-by-step solution

Step 1. Definition 

if$j$and$n$are integers with$0\le j\le n$, the symbol$\left(\begin{array}{c}n\\ j\end{array}\right)$is defined as$\left(\begin{array}{c}n\\ j\end{array}\right)=\frac{n!}{j!\left(n-j\right)!}$

Step 2. Explanation 

$\Rightarrow$$\left(\begin{array}{c}7\\ 3\end{array}\right)=\frac{7!}{3!\left(7-3\right)!}$

$\Rightarrow \left(\begin{array}{c}7\\ 3\end{array}\right)=\frac{7\times 6\times 5\times 4\times 3\times 2\times 1}{\left(3\times 2\times 1\right)\left(4\times 3\times 2\times 1\right)}$

$\Rightarrow \left(\begin{array}{c}7\\ 3\end{array}\right)=35$