Question

$\left(\begin{array}{c}n\\ 0\end{array}\right)=\dots \dots$and$\left(\begin{array}{c}n\\ 1\end{array}\right)=\dots \dots$

Short answer

The value of$\left(\begin{array}{c}n\\ 0\end{array}\right)=1$and$\left(\begin{array}{c}n\\ 1\end{array}\right)=n$

Step-by-step solution

Step 1. Explaining first part

$\Rightarrow \left(\begin{array}{c}n\\ 0\end{array}\right)=\frac{n!}{0!\left(n-0\right)!}$

$\Rightarrow \left(\begin{array}{c}n\\ 0\end{array}\right)=\frac{n!}{n!}=1$

Step 2. Explaining second part

$\Rightarrow \left(\begin{array}{c}n\\ 1\end{array}\right)=\frac{n!}{1!\left(n-1\right)!}$

$\Rightarrow \left(\begin{array}{c}n\\ 1\end{array}\right)=\frac{n\left(n-1\right)!}{\left(n-1\right)!}=n$