Question

How to find permutation or combination of ${}^7{C}_4$

Answer 1

Evaluate the value of given expression

By using the formula

$\begin{array}{rcl}\mathbf{}\mathbf{}\mathbf{}{\mathbf{}}^{\mathbf{n}}{\mathit{C}}_{\mathbf{r}}& \mathbf{=}& \frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\mathbf{(}\mathbf{n}\mathbf{-}\mathbf{r}\mathbf{)}\mathbf{!}}\\ {\Rightarrow }^7{C}_4& =& \frac{7!}{4!\left(7-4\right)!}\\ & =& \frac{7!}{4!3!}\\ & =& \frac{5\times 6\times 7}{2\times 3}\\ & =& 35\end{array}$

Hence, the value of ${}^{\mathbf{7}}{\mathit{C}}_{\mathbf{4}}$ is $\mathbf{35}$.