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Find all combinations of 6 items. Any order, no repeats.

  1. Apr 11, 2013 #1
    This may be simple but I want to see a formula and admit I've been out of school too long to figure this one out. Although it's bugging me! I would like to see a formula, too, not just the answer.

    So you have 6 items. For example ABCDEF.
    You must use at least one item.
    Order does not matter (ie. ABC=ACB)
    They can not repeat.

    So how many different combinations can I create with these items?

    Thanks in advanced!
  2. jcsd
  3. Apr 11, 2013 #2


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    Science Advisor

    1 item - 6, 2 items - 6x5/2, 3 items - 6x5x4/(3x2), 4 items - same as 2, 5 items - same as 1, 6 items - 1.

    It is basically binomial coefficients.
  4. Apr 11, 2013 #3
    If you don't care to break out the number of combinations based on the number of items in each group (as done by mathman), it's even simpler. Each item either is or is not included, so there are 2^6 possibilities. But you want at least one item in each selection, so subtract 1 to account for the empty set. Solution: 2^6 - 1.
  5. Apr 12, 2013 #4
    Thanks guys I knew it was something so simple. As a designer I don't use math much anymore although it was always one of my favorite subjects in school.

    This is great because this was based on a real life situation of creating images of these groups for a client. I created 60 so I see now that I'm missing 3.
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