jamessinatraaa

2021-12-27

How do you evaluate $8{C}_{2}$?

autormtak0w

Expert

Explanation:
We have, $n{C}_{r}=\frac{n!}{\left(n-r\right)!r!}$
$\therefore 8{C}_{2}=\frac{8!}{\left(8-2\right)!\cdot 2!}=\frac{8!}{6!\cdot 2!}=\frac{6!\cdot 7\cdot 8}{6!\cdot 2!}=\frac{7\cdot 8}{2!}=\frac{56}{1\cdot 2}=28$

Barbara Meeker

Expert

In the given problem, we have to evaluate $8{C}_{2}$ Here, we will use the formula of combination which is
$n{C}_{r}=\frac{n!}{\left(n-r\right)!r!}$ You can easily identify that n is 8 and r is 2 here.
$⇒8{C}_{2}=\frac{8!}{\left(8-2\right)!2!}$
$=\frac{8!}{6!2!}$
$=\frac{8×7×6!}{6!2!}$
After calculating the above e\times pression, we get
$=\frac{8×7}{2!}$
$=\frac{8×7}{2×1}$
$=\frac{56}{2}$
$=28$
Therefore, $8{C}_{2}=28$

Vasquez

Expert