Combinations! How many.

  1. Combinations! How many.........

    1. The problem statement, all variables and given/known data
    How many letter combinations with 9 letters are you able to make with following letters : M-A-T-E-M-A-T-I-K?


    2. Relevant equations
    Well its pretty obvious you need to use Combinations.

    Please explain how you solve this problem, don't write use combinations :smile:.
    I need to know how you think and from which angle you "attack" the problem.
     
  2. jcsd
  3. Dick

    Dick 25,893
    Science Advisor
    Homework Helper

    You have 9 letter positions to fill. First lets place the M's. There are two of them, so I have C(9,2) ways. Now lets do the A's. There 2 of them and 7 places left to fill, so I have C(7,2) ways. So far I've got C(9,2)*C(7,2). Can you finish?
     
  4. So iit´s C(9,2)*C(7,2)*C(5,2)*3*2*1?

    In my math book the answer is C(9,2)*C(7,2)*5!..... which i find a little strange.
     
  5. danago

    danago 1,125
    Gold Member

    When i did it, i got the same answer as you, and then to check, i got mathematica to output every single permutation of those letters into a list. That list contained 45360 elements, so unless ive misunderstood the question, it seems that you may be right.
     
  6. Hurkyl

    Hurkyl 16,089
    Staff Emeritus
    Science Advisor
    Gold Member

    Did you notice those are the same thing?

    Incidentally, it seemed most clear to me to write the answer as
    9! / (2! * 2! * 2!),​
    or, as a multinomial coefficient,
    [tex]\binom{9}{2 \ 2 \ 2 \ 1 \ 1 \ 1} .[/tex]​
     
    Last edited: Jun 3, 2007
  7. Dick

    Dick 25,893
    Science Advisor
    Homework Helper

    They aren't the same thing. They differ by a factor of two. Whoever wrote the solution seems to have miscounted the number of doubled letters.
     
  8. Hurkyl

    Hurkyl 16,089
    Staff Emeritus
    Science Advisor
    Gold Member

    Ah, right. This is what was written:
    C(9,2)*C(7,2)*C(5,2)*3*2*1​
    and this is what I thought I read:
    C(9,2)*C(7,2)*C(5,2)*3!*2!*1!​
     
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