Question

Evaluate the expression $$C(8,3)$$.

Answer 1

Evaluate the expression $$C(8,3)$$:

Given, $$C(8,3)$$

Definition of Combination:

A combination is a mathematical technique that determines the number of possible arrangements in a collection of items where the order of the selection does not matter.

We know the formula for the combination that can be expressed as,

$C\left(n,r\right)=\frac{n!}{r!\left(n-r\right)!}$

Then,

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

Hence, the value of $$C(8,3)$$ is $56$.