Question

The value of ${}^{8}C_3$ is equal to ?

• A. $18$
• B. $56$
• C. $28$
• D. $65$

Answer 1

The correct option is B

$56$

Explanation for the correct option:

Value of binomial coefficient:

Given, ${}^{8}C_3$

We know that, ${}^{n}C_r=\frac{n!}{r!(n-r)!}$

So,

$$\begin{gathered} {}^{8}C_3=\left[\frac{8!}{(8-3)!3!}\right] \\ =\left[\frac{8!}{5!3!}\right] \\ =\left[\frac{8\times 7\times 6\times 5\times 4\times 3\times 2\times 1}{\left(5\times 4\times 3\times 2\times 1\right)\times \left(3\times 2\times 1\right)}\right] \\ =\left[\frac{8\times 7\times 6}{\left(3\times 2\times 1\right)}\right] \\ =56 \end{gathered}$$

Hence, the correct answer is option (B).