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Ways to place molecules

  1. Aug 26, 2005 #1

    I'm not quite sure about this question:

    'How many Ways can 6 distinguishable molecules be placed in 3 different energy levels with 3 molecules in the 1st level, 2 in the 2nd level and 1 in the 3rd level, ignoring energy required?'

    If it was just how many ways to place them in 3 different levels it would be easy but how to always keep 3 molecules in the first, 2 in the 2nd and 1 in the first confuses me.

    I know that the number of Ways is less than before and I'm thinking along the lines of having to divide the number obtained if it was just 3 different energy levels, by 3!2!1! (the number of molecules in each level). This gives: W=10 which I think is very wrong!

    Any help appreciated!

  2. jcsd
  3. Aug 26, 2005 #2


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    Take a slightly more general question:

    How many ways can N numbered balls be grouped into three sets such that the first group contains [itex]n_1[/itex] balls, the second set [itex]n_2[/itex] balls and the third set [itex]N-n_1-n_2[/itex] balls?

    Hint: How many ways are there to choose the first set? After that, in how many ways can you choose the second set?
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