Permutations and Combinations – How to Tell the Difference

Have you ever taught permutations and combinations?

Do you use the words, “In permutations, order matters”?

There are lots of permutation problems where there’s no ordering whatsoever. But they are still permutations. So telling the difference between a combination and permutation can be difficult if you use the ol’ “order matters” rule. Like this:

Notice there was no “order” in the permutation – each cat is having something different done with it. (And woe for the cat who’s being eaten.)

The real differentiating factor between permutations and combinations is this:

If the things being chosen are going to do (or have done to them) the same thing, it’s a combination.

and

If the things being chosen will do (or have done to them) different things, it’s permutation.

Here’s another example, along with a tip to choosing which to use:

Will this help your students? And check out the next post on how to do the calculations for these.