Question

Evaluate each expression

$C\left(12,7\right)$

Short answer

The value of $C\left(12,7\right)=792$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $C\left(12,7\right)$.

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 $n=12,r=7$

Plugging the values:

$\begin{array}{l}C\left(12,7\right)=\frac{12!}{\left(12-7\right)!7!}\\ C\left(12,7\right)=\frac{12!}{5!7!}\\ C\left(12,7\right)=\frac{12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7!}{5\cdot 4\cdot 3\cdot 2\cdot 1\cdot 7!}\\ C\left(12,7\right)=792\end{array}$

Step 3. Conclusion.

Hence, the value of $C\left(12,7\right)=792$.