# Thread: Permutation or Combination?

1. ## Permutation or Combination?

I was wondering if someone could offer some guidance as to whether this problem is a permutation or combination.

A newcomers' club of 30 people wants to choose an executive board consisting of president, secretary, treasurer, and 2 other officers. In how many ways can this be accomplished?

To me, it seems as though this would be a permutation because the order of the officers matters because each has a distinct job.
P(30,5)=(30)(29)(28)(27)(26)=17100720

I am not sure though. What do you think?

2. Originally Posted by discretec
I was wondering if someone could offer some guidance as to whether this problem is a permutation or combination.

A newcomers' club of 30 people wants to choose an executive board consisting of president, secretary, treasurer, and 2 other officers. In how many ways can this be accomplished?
Order does matter for three of the positions.
$\displaystyle ^{30}\mathcal{P}_3\cdot ^{27}\mathcal{C}_2$.

3. Originally Posted by Plato
Order does matter for three of the positions.
$\displaystyle ^{30}\mathcal{P}_3\cdot ^{27}\mathcal{C}_2$.
Thanks, I also thought that could be possible, but was not sure. I appreciate your help.