What is the difference between a combination and permutation?

1 Answer
Feb 16, 2016

For permutations order matters, whereas for combinations it doesn't.


It's all about order with combinations and permutations. Sometimes when you choose values randomly to form a set it matters what the order of the values is and sometimes it doesn't. That is the difference between permutations and combinations.

Imagine we have a bowl of bingo balls. There are 10 balls each numbered 0, 1, ..., 9. Imagine now that we select 2 balls at a time and then replace them before repeating. How many different ways could we get different combinations of balls?

If we are counting permutations, then drawing a 1 and then a 2 is different than drawing a 2 and then a 1. Whereas, if we are counting combinations, no matter how we end up with a 1 and a 2, it is the same.

Therefore there are always fewer combinations than permutations.