Question

How do you evaluate ${}^{6}C_4$?

Answer 1

Evaluating the required expression using the combination formula.

As we know that, a combination is a grouping or subset of items.

We will evaluate the given expression ${}^{6}C_4$ by using the combination formula.

The order does not matter in a combination.

So,

$\Rightarrow$ $C\left(n,r\right)={}^{n}C_r$

$\Rightarrow$ ${}^{n}C_r=\frac{n!}{\left(n-r\right)!r!}$

Here, $n$ is the number of items in set and $r$ is the number of items selected from the set.

So,

$\Rightarrow$ ${}^{6}C_4=\frac{6!}{\left(6-4\right)!\times 4!}$

$\Rightarrow$ ${}^{6}C_4=\frac{6\times 5\times 4!}{2\times 1\times 4!}$

$\Rightarrow$ ${}^{6}C_4=15$

Hence the simplified form of expression ${}^{6}C_4$ is $15$.