Question

How do you evaluate ${}^{8}C_2$ ?

Answer 1

Evaluating the function.

As we know, in Mathematics, ${}^{n}P_r$ and ${}^{n}C_r$ are the probability functions that shows the permutations and combinations.

We will evaluate the given function ${}^{8}C_2$ by using the formula is,

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

Here, $C$ is the number of combinations, $n$ is the total number of objects in the set and $r$ is the number of choosing objects from the set.

Therefore,

$\Rightarrow$ ${}^{8}C_2=\frac{8!}{\left(8-2\right)!\times 2!}$

$\Rightarrow$ ${}^{8}C_2=\frac{8!}{6!\times 2!}$

Factoring the term $8!,2!$ and $6!$.

We will simplify the expression by factoring the term $8!,2!$ and $6!$.

$\Rightarrow$ ${}^{8}C_2=\frac{6!\times 7\times 8}{6!\times 2}$

$\Rightarrow$ ${}^{8}C_2=\frac{56}{1\times 2}$

$\Rightarrow$ ${}^{8}C_2=28$

Hence, the simplified form of ${}^{8}C_2$ is $28$.