Question

How many ways can a president, vice-president, secretary, and treasurer be chosen from a club with 8 members?

Answer 1

$_8C_4=\dfrac{8!}{4!4!}=\dfrac{5\cdot6\cdot7\cdot8}{2\cdot3\cdot4}=70$

Answer 2

Answer with explanation:

There are four members ,president, vice-president, secretary, and treasurer, which need to be chosen from 8 members.

As order of chosing the members from 8 members is not important.

So, Possible number of ways

         $=_{4}^{8}\textrm{C}\\\\=\frac{8!}{(8-4)!4!}\\\\=\frac{8*7*6*5*4!}{4!*4!}\\\\=\frac{8*7*6*5}{4*3*2*1}\\\\=7*2*5\\\\=70 \text{Ways}$