Question

Evaluate each expression

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

Short answer

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

Step-by-step solution

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