What is a permutation?

Answer 1

In general, the idea of a permutation is of a re-ordering of things, of the elements of a set. It may be looked at as mapping or correlating, but it usually can be though of as rearranging the elements of a set in different ways. Let's look at some examples and see what's up. How many ways are there to arrange the first three positive integers? The numbers 1, 2, and 3 can be arranged in a number of different ways. Each way is a permutation of the original set of numbers. 123, 132, 213, 231, 312, 321 are the ways. How many different hands are possible when being dealt 5 cards from a deck of 52 playing cards? It turns out that there are 311,875,200 ways to deal five cards. That's 311,875,200 permutations of five cards from a 52 card deck. Note that there are only 2,598,960 distinct hands or combinations of cards because the order the cards are dealt in doesn't matter in the actual play of the cards. If your first four cards are the aces of each suit, that's one hand, but they can be dealt to you in 24 different ways, or 24 different orders or 24 different permutations. There are advanced concepts that permit us to do things with sets under the heading of permutations. But the basics are presented here, and they and other ideas on permutations can be reviewed by Surfing on over to the Wikipedia article on permutaitons. A link is provided.