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so my answer is (202 choose 2)

But if baskets were identical? Should we first choose a basket where to put some coins?

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    If the baskets are identical, you have to break into cases: 1) Two baskets have the same number of coins 2) All baskets have a different number of coins. – Arthur Jan 25 '18 at 12:18
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    Are the coins indistinguishable? – Bram28 Jan 25 '18 at 12:36
  • Refer to Stefen's answer in the question. https://math.stackexchange.com/questions/2619042/circular-permutations-with-alike-objects. I know the question is different but on careful reading you will understand that the method to solve is very similar – Rohan Shinde Jan 25 '18 at 14:15
  • 202 choose 2 counts the ways to split 200 indistinguishable coins into 3 baskets, so it looks like coins are indistinguishable. – Air Conditioner Jan 25 '18 at 14:54
  • The number of placements of n indistinguishable objects into x indistinguishable baskets is counted by the integer partitions of n into $\leq$ x parts. – Air Conditioner Jan 25 '18 at 15:04

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