Question

Evaluate each expression

$C\left(10,4\right)$

Short answer

The value of $C\left(10,4\right)=210$.

Step-by-step solution

Step 1. Given Information.

Given to evaluate the expression $C\left(10,4\right)$.

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=10,r=4

Plugging the values:

$\begin{array}{l}C\left(10,4\right)=\frac{10!}{\left(10-4\right)!4!}\\ C\left(10,4\right)=\frac{10!}{6!4!}\\ C\left(10,4\right)=\frac{10\cdot 9\cdot 8\cdot 7\cdot 6!}{6!\cdot 4\cdot 3\cdot 2\cdot 1}\\ C\left(10,4\right)=210\end{array}$

Step 3. Conclusion.

Hence, the value of $C\left(10,4\right)=210$.