Question

Evaluate each expression

$C\left(9,3\right)·C\left(6,2\right)$

Short answer

The value of $C\left(9,3\right)·C\left(6,2\right)=1260$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $C\left(9,3\right)·C\left(6,2\right)$.

Step 2. Calculation.

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

Using the formula:

$\begin{array}{l}C\left(9,3\right)\cdot C\left(6,2\right)=\frac{9!}{\left(9-3\right)!3!}\cdot \frac{6!}{\left(6-2\right)!2!}\\ C\left(9,3\right)\cdot C\left(6,2\right)=\frac{9!}{6!3!}\cdot \frac{6!}{4!2!}\\ C\left(9,3\right)\cdot C\left(6,2\right)=\frac{9\cdot 8\cdot 7\cdot 6\cdot 5\cdot 4!}{6!\cdot 3\cdot 2\cdot 1}\cdot \frac{6!}{4!\cdot 2\cdot 1}\\ C\left(9,3\right)\cdot C\left(6,2\right)=1260\end{array}$

Step 3. Conclusion.

Hence, the value of $C\left(9,3\right)·C\left(6,2\right)=1260$.