Combinations and Permutations of Cards

[Baron]

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

 

[mathman]

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.

 

[Baron]

Thanks,0 is not allowed

 

[Baron]

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)

 

[mathman]

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.