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Combination question

  1. Mar 4, 2014 #1
    1. The problem statement, all variables and given/known data


    In how many ways can 8 different things be divided into groups of 5 and 3.


    2. Relevant equations



    3. The attempt at a solution

    I thought it be just be 8C5 X 8C3

    but also might it be 8C5 x 3C3 since if you take 5 you only have 3 left to select from?
     
  2. jcsd
  3. Mar 4, 2014 #2

    Ray Vickson

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    If you pick the three for one group you automatically leave 5 for the other group.
     
  4. Mar 4, 2014 #3

    HallsofIvy

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    Another way to look at this is to arrange the 8 items in a row, then label those to go into the first group "0" and those to go into the second group "1". How many different way are there to order 5 "0"s and 3 "1"s?
     
  5. Mar 4, 2014 #4
    Thank you
     
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