Permutation questions- urgent help needed

DrSteve
Thu, 24 Jan 2013 12:01:23 +0000

@pckeller

I always work under the assumption that writing things in different orders gives distinct objects unless specified otherwise. For example, if someone were to tell me that prime factorizations are unique, I would say “no they’re not 6=23=32. Prime factorizations are only unique up to order!” That said, I do believe you’re right. Without showing an example, the problem may be unclear, especially since addition is commutative and all.

That said, I think if you write out 2 or 3 more examples you’ll be able to see what the formula is. Note that there are (at least) 2 ways to recognize this formula - the first is simply by pattern recognition (after looking at enough examples), and the second is by actually thinking about what you’re counting (again, I think some examples might be necessary to realize this). Only the second of the 2 gives a deductive argument that the formula is actually correct (although I’m sure many other proofs will work - mathematical induction comes to mind).