Question

How do you evaluate ${}^{9}C_3$?

Answer 1

Evaluate the given term?

${}^{n}C_r=\frac{n!}{r!\times \left(n-r\right)!}$

Values of $n$and $r$

$$\begin{gathered} n=9 \\ r=3 \end{gathered}$$

Substitute $n$ and $r$ values in the above formula

$$\begin{gathered} {}^{9}C_3=\frac{9!}{3!\times \left(9-3\right)!} \\ =\frac{9!}{3!\times 6!} \\ =\frac{9\times 8\times 7\times 6!}{(3\times 2\times 1)\times 6!} \\ =84 \end{gathered}$$

Hence the answer is $84$