Question

How do you evaluate${}^{8}C_3$?

Answer 1

Find the value of the given term?

Use the following formula to calculate the value

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

$$\begin{gathered} n=8 \\ r=3 \end{gathered}$$

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

$$\begin{gathered} {}^{8}C_3=\frac{8!}{3!\times \left(8-3\right)!} \\ =\frac{8!}{3!\times 5!} \\ =\frac{8\times 7\times 6\times 5!}{(3\times 2\times 1)\times 5!} \\ =56 \end{gathered}$$

Hence the answer is $56$