Question

Evaluate$\left(\begin{array}{c}60\\ 20\end{array}\right)$

Short answer

The value of$\left(\begin{array}{c}60\\ 20\end{array}\right)=4191844505805494$

Step-by-step solution

Step 1. Defination

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

$\Rightarrow \left(\begin{array}{c}60\\ 20\end{array}\right)=\frac{60!}{20!\left(60-20\right)!}$

$\Rightarrow \left(\begin{array}{c}60\\ 20\end{array}\right)=\frac{60\times 59\times 58\cdots \cdots \times 1}{\left(20\times 19\times 18\cdots \cdots \times 1\right)\left(40\times 39\times 38\cdots \cdots \times 1\right)}$

$\Rightarrow \left(\begin{array}{c}60\\ 20\end{array}\right)=4191844505805494$