couunting and probability

Hello. You seem to be missing some information!

I got this question before, too. So I will assume that you have the same one:

Our club has 25 members, and wishes to pick a president, secretary, and treasurer. In how many ways can we choose the officers, if individual members are allowed to hold 2 but not all 3 offices?

Since this is an AoPS question, I'll give you a start-up but not the whole solution.

Here, we would use permutations. However, what will be different from the regular question, is one person can hold two positions.