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How many ways can you arrange 52 things into 4 groups BUT th

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  1. Dec 15, 2015 #1
    How many ways can you arrange 52 things into 4 groups BUT the groups do not have to be the same size?!?
     
  2. jcsd
  3. Dec 15, 2015 #2
    If the things are distinguishable and the groups are distinguishable and a group can be zero size and the order within a group doesn't matter, ##4^{52}##.
     
  4. Dec 15, 2015 #3

    WWGD

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    If I understood correctly, this is the problem of balls in boxes, where you want to put 52 objects in 4 boxes. If the things are indistinguishable, then the answer is the solution to ## x_1+x_2+x_3+x_4=52 ## , which is equal to ## (n+k-1)C(k-1) ## , where ##C## stands for "choose", as in " x choose k":= ##\frac {x!}{k!(x-k)!} ## .
     
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