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Calculate the numbers of ways to arrange 6 letters out of 7 letters of

  1. Apr 14, 2012 #1
    Calculate the numbers of ways to arrange 6 letters out of 7 letters of the word `SETTEES'.
    Answer:210
    Could anyone explain this to me ?thx
     
  2. jcsd
  3. Apr 14, 2012 #2

    pcm

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    Re: permutation.SOS

    try making different cases, for example 3 alike of 1 kind 2 alike of another kind and 1 of third kind.
    or if you have read multinomial theorem try using that.it is simpler.
     
  4. Apr 14, 2012 #3

    jambaugh

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    Science Advisor
    Gold Member

    Re: permutation.SOS

    I find it most helpful to go through the mental process of actually choosing an arrangement and counting the choice one makes at each stage. You multiply the numbers for each stage to get the total multiplicity of choices. You then consider if you created any equivalent arrangements and divide those out. Example: Arrangements of two of the letters "ADD".

    First I would distinguish the two D's { A, D1, D2}.
    There are three letters and I have 3 choices for the first in my arrangement. There are two remaining and I have 2 choices for the 2nd. That's 3 x 2 = 6 choices.

    Now since we can't really distinguish D1 vs D2 we divide out the ways we may have multiply chosen the same arrangement.

    Of those 6 arrangements starting with any of the 2 permutations of D1 and D2 will give me an identical sequence of choices. So I divide by 2!=2 6/2 = 3.
    AD DA and DD.

    In your case there are 3!=6 ways to permute the three E's times 2!=2 ways to permute the S's and 2!=2 ways to permute the T's. That's 6x2x2=24 equivalent starting configurations. Figure the way to arrange 6 of 7 distinct letters and then divide by 24.
     
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