Question

Evaluate each expression

$C\left(5,2\right)$

Short answer

The value of $C\left(5,2\right)=10$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $C\left(5,2\right)$.

Step 2. Calculation.

When n objects are available and r are to be picked then the number of combinations is given by $C\left(n,r\right)=\frac{n!}{\left(n-r\right)!r!}$

Here n=5,r=2

Plugging the values:

$\begin{array}{l}C\left(5,2\right)=\frac{5!}{\left(5-2\right)!2!}\\ C\left(5,2\right)=\frac{5!}{3!2!}\\ C\left(5,2\right)=\frac{5\cdot 4\cdot 3!}{3!\cdot 2\cdot 1}\\ C\left(5,2\right)=\frac{20}{2}\\ C\left(5,2\right)=10\end{array}$

Step 3. Conclusion.

Hence, the value of $C\left(5,2\right)=10$.