Question

Use the formula $C(n,r)=\frac{n!}{(n-r)!r!}$to find the value of each combination.

$C(7,4)$

Short answer

The value of the given combination is 35.

Step-by-step solution

Step 1. Given information.

The given combination is $C(7,4)$.

Step 2. Determine the value of the given combination.

Using the formula, the given combination can be written as:

$\begin{array}{rcl}C(7,4)& =& \frac{7!}{(7-4)!4!}\\ & =& \frac{7!}{3!4!}\\ & =& \frac{7\times 6\times 5\times 4!}{3\times 2\times 1\times 4!}\\ & =& 35\end{array}$

Step 3. Conclusion.

The value of the given combination is 35.