A club has 16 members. In how many ways can 3 officers consisting of a president, vice-president, and secretary be chosen? Fill in the blank with your answer which should be a positive integer

Question

anonymous · Answer

So how many different ways can you permute 3 people from a set of 16?

anonymous · Answer

It's not a combination, because the order matters. The first chosen will be president, etc.

anonymous · Answer

how would i set this up?

anonymous · Answer

Lets say you start by picking the president. How many different ways can you choose him?

anonymous · Answer

Or her =)

anonymous · Answer

im confused

anonymous · Answer

I argue that:

There are 16 possible candidates for president. Therefore there are 16 different ways you could choose it.

Then there are 15 different ways you can choose vice president.

Then there are 14 different ways you can choose secretary.

Since you must do all 3, by the product rule there are

16*15*14 different ways you can elect these 3 positions.

This is 16!/13!  or 16P3. 

It is not 16C3 which is much smaller.