[tex]_8C_4=\dfrac{8!}{4!4!}=\dfrac{5\cdot6\cdot7\cdot8}{2\cdot3\cdot4}=70[/tex]
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
[tex]=_{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}[/tex]