Question

How many ways can a president, vice-president, secretary, and treasurer be elected from a group of 25 students if each student is eligible for each office?

Answer 1

just filling four spaces :

25 x 24 x 23 x 22

Answer 2

You're interested in ways to pick 4 students out of a group of 25 *with attention paid to order*, which is equivalent to ways of making permutations of 4 students from a pool of 25. The answer is then just \(_{25}P_4=\dfrac{25!}{(25-4)!}=25\times24\times23\times22\)