Q16. - Algebra 2

Question

Evaluate each expression

 

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

Step-by-Step Solution

Answer

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

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