Question

Evaluate$\left(\begin{array}{c}50\\ 49\end{array}\right)$

Short answer

The value of$\left(\begin{array}{c}50\\ 49\end{array}\right)=50$

Step-by-step solution

Step 1. Defination

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

Step 2. Explanation

$\Rightarrow \left(\begin{array}{c}50\\ 49\end{array}\right)=\frac{50!}{49!\left(50-49\right)!}$

$\Rightarrow \left(\begin{array}{c}50\\ 49\end{array}\right)=\frac{50\times 49\times 48\times 47\cdots \cdots \times 1}{\left(49\times 48\times 47\cdots \cdots \times 1\right)\left(1\right)}$

$\Rightarrow \left(\begin{array}{c}50\\ 49\end{array}\right)=50$