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Permutations and Combinations

  1. May 6, 2008 #1
    1. The problem statement, all variables and given/known data
    The letters of the word POSSESSES are written on 9 cards, one on each card. The cards are shuffled and four of them are selected and arranged in a straight line.

    2. Relevant equations

    (a) how many possible selections are there of 4 letters?
    (b"how many arrangements are there of 4 letters?


    3. The attempt at a solution

    Well first of all, how do you start of a question like this. for the first part(a)
    9C4=126 but here i see there are 5 s's and 2 e's. how can i apply the formula to this question. because there are 5 s's and 2e's so this forumla is invalid.

    for arrangements for 9 words. 9!/5!2! but this is for the 9 letters. i am only focusing on the four words being selected. how can i start
     
  2. jcsd
  3. May 6, 2008 #2
    the problem here is that all the letters are not different. there are two e's and 5s's how do you approach the question when the letters are repeated.
     
  4. May 6, 2008 #3
    I do not know a simple way of doing this, but there is little enough that you can crunch through it with casework. Separate cases based on repetitions of letters. For example, one case would be the possible arrangements with 4 S's. Another could be the possible arrangements with 2 S's and 2 E's, etc.
     
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