Results 1 to 2 of 2

Math Help - Combination or Permutation?

  1. #1
    Newbie
    Joined
    Jan 2009
    Posts
    9

    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?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Grandad's Avatar
    Joined
    Dec 2008
    From
    South Coast of England
    Posts
    2,570

    Arrangements with repeated letters

    Hello Lupin
    Quote Originally Posted by Lupin View Post
    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 L_1, I, T_1, T_2, L_2, E - then there would be 6! arrangements.

    But the L_1 and L_2 are indistinguishable. And they can be arranged among themselves in 2! = 2 ways. So our 6! arrangements will contain each of these 2! arrangements as if they were different. And, of course, they're not. So we need to divide by 2!.

    And the same goes for T_1 and T_2: we need to divide by 2! again, to get rid of the duplication caused by the T's.

    So the final answer is that there are \frac{6!}{2!2!} = 180 different arrangements.

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

    \frac{n!}{a!b!...}

    Grandad
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. combination/permutation
    Posted in the Discrete Math Forum
    Replies: 0
    Last Post: October 16th 2008, 11:40 PM
  2. permutation and combination
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 11th 2008, 07:42 AM
  3. Permutation and Combination
    Posted in the Statistics Forum
    Replies: 2
    Last Post: September 28th 2008, 09:37 PM
  4. Permutation and Combination
    Posted in the Statistics Forum
    Replies: 5
    Last Post: February 16th 2008, 01:17 PM
  5. Combination/Permutation
    Posted in the Statistics Forum
    Replies: 6
    Last Post: September 11th 2007, 03:42 PM

Search Tags


/mathhelpforum @mathhelpforum