Question

Decide whether you would use a permutation, a combination, or neither. Next, write the solution using permutation notation or combination notation, if possible, and, finally, answer the question.

A club with 31 members is to select five officers (president, vice president, secretary, treasurer, and historian). In how many ways can this be done?
I came up with 155 ways,
Thank you and Good afternoon

Answer 1

It is not combinations because the order matters, it is permutations. (Joe could be either president or vice president for example and those are not the same)
31!/(31-5)!
= 31!/26!
= 31*30*29*28*27
= 20,389,320

Answer 2

thank you Damon I took notes to see how if falls into place.

Answer 3

You are welcome.
This is a good example to diiferentiate between combinations and permutations

Combinations of 31 taken 5 at a time would be
31! /[ 5! (31-5)! ]

That takes into account all the different groups of five you can make, but does not order the five for specific office.

If you now require a different choice for every office within the group of 5, you will get 5! or 120 times as many arrangements
20,389,320 / 120 = 169,911
so I do not know where you got 155