Q7. - Algebra 2

Question

Evaluate each expression

 

$C\left(6,1\right)$

Step-by-Step Solution

Answer

The value of $C\left(6,1\right)=6$.

Step 1. Given Information.

Given to evaluate the expression $C\left(6,1\right)$.

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=6,r=1

Plugging the values:

 $\begin{array}{l}C\left(6,1\right)=\frac{6!}{\left(6-1\right)!1!}\\ C\left(6,1\right)=\frac{6!}{5!1!}\\ C\left(6,1\right)=\frac{6\cdot 5!}{5!\cdot 1}\\ C\left(6,1\right)=\frac{6}{1}\\ C\left(6,1\right)=6\end{array}$

Step 3. Conclusion .

Hence, the value of  $C\left(6,1\right)=6$.