What is the total permutation equation with a set of distinct permutation combinations?

Question

I am working on a game where there is always 4 opponents. Each opponent is one of 4 classes and there is always 1 of each class. I want to know how many permutations are possible given an equal distribution of units per class.

For example. If I had 120 enemies and I wanted to do any random factorial it would be 120 choose 4. But since I want to have a combination of classes evenly, it would be "1 choose 30 x 4."

Do you know how I can calculate the total permutations in this scenario?

Thank you.

score 1 · Accepted Answer · answered Apr 01 '20 at 01:44

1

If there are $30$ enemies of each kind and you choose one of each there are $30^4$ combinations. If there is an order to them, say the five of you are in a circle, multiply by $4!$ for the order of the four.

answered Apr 01 '20 at 01:44

Ross Millikan

374,822

Ahh so its an exponential in this case. Thank you – Aggressor Apr 01 '20 at 11:36
It is the multiplication principle. If there were $36$ on one kind, $24$ of the second, $31$ of the third, and $20$ of the fourth, it would be $36 \cdot 24 \cdot 31 \cdot 20$ – Ross Millikan Apr 01 '20 at 13:09
I think I got so hung up on permutations I made this far more complicated a problem than it was. – Aggressor Apr 01 '20 at 13:11

What is the total permutation equation with a set of distinct permutation combinations?

1 Answers1