Math for Elementary Teachers II 1512

Permutations

So what is a permutation exactly? Well it is the combination that something occurs, and more importantly the combination and which they occur are important. It's not just the different combinations something occurs, it has a specific order in which they occur; in other words a permutation is a ordered combination.

So what is the difference in a way that is easy to understand? Well basically if you think of it like it is a combination lock it will help you understand. You can only put the exact combination into a combination lock for it to open. When calculating permutation it is basically the same thing. You can only use the different options in a specific order.

Consider the following:

Given 3 people, Joe, Tiffany and Sue, how many different ways can these three people be arranged where order matters?
Let JTS stand for the order of Joe on the left, Tiffany in the middle and Sue on the right.
Since order matters, a different arrangement is JTM. Where Joe is on the left, Sue is in the middle and Tiffany is on the right.
If we find all possible arrangements of Joe, Tiffany and Sue where order matters, we have the following possibilities:

JTS, JST, TSJ, TJS, STJ, SJT

The number of ways to arrange three people three at a time is:
3! = (3)(2)(1) = 6 ways