Question

Find the value of ${}^{10}C_3$

Answer 1

Solve for the required value

Given ${}^{10}C_3$

We know that,

$$\begin{gathered} {}^{\mathbf{n}}\mathit{C}_{\mathbf{r}}\mathbf{=}\frac{\mathbf{n}\mathbf{!}}{\mathbf{r}\mathbf{!}\left(n-r\right)\mathbf{!}} \\ \Rightarrow {}^{10}C_3=\frac{10!}{3!\left(10-3\right)!} \\ =\frac{10!}{3!7!} \\ =\frac{10\times 9\times 8\times 7!}{3\times 2\times 1\times 7!} \\ =120 \end{gathered}$$

Hence, the value of ${}^{10}C_3$ is $120$