SOLUTION
A president, vice-president, secretary, and treasurer are 4 persons.
So we want to know in how many ways these 4 persons can be chosen from 8, we have
[tex]\begin{gathered} ^8P_4 \\ =\frac{8!}{(8-4)!} \\ =\frac{8\times7\times6\times5\times4!}{4!} \\ =8\times7\times6\times5 \\ =1,680\text{ ways } \end{gathered}[/tex]Hence the answer is option C
