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Combinations and Permutations of Cards

  1. Mar 23, 2013 #1
    Hey guys,
    I have a problem relating to combinations and permutations.In how many ways can I divide a deck of 52 cards into piles of 3 with each pile containing any number?
    for example 50,1,1 or 45,6,1
    Thanks in advance
     
  2. jcsd
  3. Mar 24, 2013 #2

    mathman

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    Is 0 allowed for one of the piles? If you look at in two steps it is fairly straightforward.
    Step 1, choose a number (k) for the first pile. There are now 52-k left for the other two piles. Assuming 0 is allowed, there are 52-k ways to split up these cards. Now just add them up for k ranging from 0 to 52. It will sum to 52x53/2.

    If 0 is not allowed, the procedure is the same, just omit the cases where any pile has 0.
     
  4. Mar 24, 2013 #3
    Thanks,0 is not allowed
     
  5. Mar 24, 2013 #4
    Can you explain this."Now just add them up for k ranging from 0 to 52".I'm a little lost.(not a math expert)
     
  6. Mar 25, 2013 #5

    mathman

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    Since 0 is not allowed. Put 50 in the first pile, then there is exactly 1 way of sorting the other two piles. Put 49 in the first pile and there are 2 ways of sorting the other 2 piles, ..., put 1 in the first pile and there are 50 ways of sorting into the other two piles. Net result 1+2+3+....+50 = (50x51)/2.
     
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