# Math Help - Permutations and combinations

1. ## Permutations and combinations

There are five members of the Math Club. In how many ways can the positions of officers, a president, and a treasurer, be chosen? I thinked it's just 5 factorial. But the answer is 20. Which means they divided by 3 factorial... Why ?

2. ## Re: Permutations and combinations

You have two offices (President, Treasurer). Now you have to choose 2 people from a group of 5 how many ways can this can be done.
Spoiler:
In $2.\binom{5}{2} = 2.\frac{5!}{2!3!} = 20$ ways. Multiplication by two is to allow permutations among them. Thanks to Evgeny (emakarov) for the correction.

3. ## Re: Permutations and combinations

Originally Posted by Shwems
There are five members of the Math Club. In how many ways can the positions of officers, a president, and a treasurer, be chosen? I thinked it's just 5 factorial. But the answer is 20. Which means they divided by 3 factorial... Why ?
See k-permutations.