How do you get the permutation of a number?

Answer 1

You can't get a permutation of a number, but you can get the permutation of a set of numbers. Take the set {1, 2, 3, 4, 5}. If you move the 1 over to the right 1 or 3 spaces and keep the other numbers in the same order, you have an odd permutation: {2, 1, 3, 4, 5} and {2, 3, 4, 1, 5} in this case. If you move the 1 over to the right 2 or 4 spaces, you have an even permutation: {2, 3, 1, 4, 5} and {2, 3, 4, 5, 1} in this case.

If two of the numbers in the set are both oddly permutated, the set as a whole is evenly permutated, kind of like how an odd number multiplied by an odd number is an even number. For example, {2, 1, 4, 3, 5} is an even permutation. However, and I'll let you figure out why on this one, {2, 1, 4, 5, 3} is an odd permutation.

There are much more formal ways to describe permutations and many different ways to write them out, as you can see by following the link below, but what I've stated above should get you started with at least a basic comprehension.