Permutation questions- urgent help needed

DrSteve
Thu, 24 Jan 2013 11:26:07 +0000

I’m not exactly sure what you mean by that. Let me give a simple example:

If j=2 and k=3, then the question becomes “in how many ways can 3 be written as a sum of 2 positive integers?”

Well let’s see: 3=1+2=2+1. So there are 2 ways.

Let’s do one more: j=2, k=4

4=1+3=2+2=3+1. So there are 3 ways.

So different choices of j and k will lead to a different answer. In other words, the answer to this question depends on j and k. Another way to say this is that the answer is a function of j and k. For example, maybe the answer is j^2+3k (it’s not). I gave you a hint. The answer can be expressed as either a simple permutation or combination with the j and k as part of the indices.

As another hint, try more specific examples until you start to see the pattern. Then ideally, by looking at your examples try to see how this is a counting problem. What exactly are you counting?