Question

How many ways can a president and a vice-president be selected from a club with 15 members if no one can hold more than one office? supposing a four year term for all offices, in how many ways can a new president and vice-president be chosen four years from now if no one is allowed to be elected to the same position twice.

I got the answer for the first part = 15P2 = 210. but not sure how to work out - in how many ways can a new president and vice-president be chosen four years from now if no one is allowed to be elected to the same position twice.

Answer 1

For the first part, you have to pick 2 people for the two posts available since one person can't have both, hence for 1st post you have 15 options to pick from. For the next post, you have 14 people to choose from, hence total possible cases are 15*14 = 210.

For the second part, the same person can' contest for the post he had earlier. Now, for the first post(let's say president) there are 14 members to choose from while for the second post(Vice-president) there are 14(excluding the vice president earlier but the president can contest for this post according to the given condition) persons to choose from. Hence total cases in this cases are 14*14 =196