Alternating permutation

An alternating permutation is like when you have a row of toys and you switch the order of some of them, but you always make sure that when you start with the first toy, you go up, then down, then up, then down, and so on. It's like you're making a wave with the toys!

For example, if you had the toys arranged in order like this:

A B C D E

And you switched B and C, it would be an alternating permutation if the order ended up like this:

A C B D E

See how the toys go up, then down, then up again? That's what an alternating permutation is!

It's not just with toys, though. You can have alternating permutations with numbers, too. Just like with the toys, you start with the first number and go up, then down, then up, then down, and so on.