Question

A hiking club has 9 members.  How many ways can they choose a president, vice president, secretary, and treasurer from among the members?

Answer 1

3024

Explanation:

The president, vice president, secretary, and treasurer have different roles. The "order" they are selected in matters.

Answer 2

`the\ variation\ without\ repetition:\\\\P(n;k)= \frac{\big{n!}}{\big{(n-k)!}} \\\\---------------------\\\\n=9\ \ \ and\ \ \ k=5\\\\\Rightarrow\ \ \ P(9;5)=\frac{\big{9!}}{\big{5!}}=\frac{\big{5!\cdot6\cdot7\cdot8\cdot9}}{\big{5!}}=3024\\\\Ans.\ there\ are\ 3024\ ways\ to\ choose.`