Thread: Combination or Permutation?

For the problem:

How many ways are there to re-arrange the letters of LITTLE?

Would I use combination, permutation or some other method? And how would I do it?

Hello Lupin

Originally Posted by Lupin

For the problem:

How many ways are there to re-arrange the letters of LITTLE?

Would I use combination, permutation or some other method? And how would I do it?

It's basically a permutation problem, but with repeated letters you need to do a bit of extra work. You do it like this:

If all 6 letters were different - call them - then there would be arrangements.

But the and are indistinguishable. And they can be arranged among themselves in ways. So our arrangements will contain each of these arrangements as if they were different. And, of course, they're not. So we need to divide by .

And the same goes for and : we need to divide by again, to get rid of the duplication caused by the 's.

So the final answer is that there are different arrangements.

You can generalise this and say that if there are items, with items repeated of the first kind, repeated of the second kind, and so on, the number of different arrangements is:



Grandad