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Multiple properties and property combinations

  1. Aug 15, 2008 #1
    Here's something I know there must be a way to easily figure out... but not by me!

    THE QUESTION...
    if I have x number of categories to choose from, how many combinations can I get?

    for example I think that if I had 4 categories there are 15 possible combinations

    categories A, B, C, D

    combinations:
    A
    B
    C
    D
    AB
    AC
    AD
    ABC
    ABCD
    BC
    BCD
    CD
    ACD
    ABD
    BD

    Am I missing any?

    so if 4 yeilds 15

    5 yields ?
    6 yields ?

    I'm know a pattern develops but how does it work? Sorry I've been out of school for so long and I don't know where to begin.:confused:
     
  2. jcsd
  3. Aug 15, 2008 #2

    mathman

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    Science Advisor
    Gold Member

    The number of subsets, of a finite set with n members, is 2n including the empty set. Omiting the empty set leaves 2n-1, which is what you got.
     
  4. Aug 18, 2008 #3
    Thanks Mathman. I knew it was some sort of sequence - 1. I just can't remember all that math I used to be so good at. Maybe I should dig up some old notes and give my brain a workout with a refresher. Hell I can't even remember my simple trig anymore :grumpy:
     
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