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## Homework Statement

You are given 8 balls, each of a different color. How many distinguishable ways can you:

(1) Divide them (equally or unequally) between 2 urns.

(2) Divide them (equally or unequally) between 2 children (and each child cares about the colors he or she receives).

## Homework Equations

These are the enumeration formulas we are responsible to know:

Sampling with replacement and order: [itex]n^r[/itex]

Sampling without replacement, without order: nCr = [itex]\frac{n!}{r!(n-r)!}[/itex]

Sampling without replacement, with order: nPr = [itex]\frac{n!}{(n-r)!}[/itex]

## The Attempt at a Solution

I initially thought that problem (1) would be without replacement and without order, so that the answer would be a combination with n=8 and r=2, and that problem (2) would be without replacement and with order, so a permutation with n=8 and r=2.

However, that isn't correct. It seems like it might actually be a case where there is replacement. The fact that we are giving the balls to two people, or placing them in two urns, is screwing me up. How can I think about this problem and go about solving it? Is it solvable with just the equations I've listed above? Thanks.