Question

Evaluate each expression.

$C\left(12,4\right)·C\left(8,3\right)$

Short answer

The value of $C\left(12,4\right)·C\left(8,3\right)=27720$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $C\left(12,4\right)·C\left(8,3\right)$.

Step 2. Calculation.

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

Using the formula:

$\begin{array}{l}C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12!}{\left(12-4\right)!4!}\cdot \frac{8!}{\left(8-3\right)!3!}\\ C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12!}{8!4!}\cdot \frac{8!}{5!3!}\\ C\left(12,4\right)\cdot C\left(8,3\right)=\frac{12\cdot 11\cdot 10\cdot 9\cdot 8\cdot 7\cdot 6\cdot 5!}{8!\cdot 4\cdot 3\cdot 2\cdot 1}\cdot \frac{8!}{5!\cdot 3\cdot 2\cdot 1}\\ C\left(12,4\right)\cdot C\left(8,3\right)=27720\end{array}$

Step 3. Conclusion.

Hence, the value of $C\left(12,4\right)\cdot C\left(8,3\right)=27720$.