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

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1. Dec 15, 2015

### Wmwhite9

How many ways can you arrange 52 things into 4 groups BUT the groups do not have to be the same size?!?

2. Dec 15, 2015

### Khashishi

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, $4^{52}$.

3. Dec 15, 2015

### WWGD

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":= $\frac {x!}{k!(x-k)!}$ .