rick.anzalone
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In how many ways can a person toss 100 (identical) dice so that at least three of each type of face be showing?
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pka
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Combin(n,k) is the combination of n different things taken k at a time: (n!)/[(k!)(n−k)!]
The answer you want is combin(82+6−1,82).
The number of ways to put I identical items into D different cells is combin(I+D−1,I).
Think of the 100 throws as identical and the six faces of the die as different cells.
If we think in terms of going ahead and put three throws in each of the six faces, then that leaves 82 more throws that can land in any one of the six cells.
This way we have at least three of each face.
The answer you want is combin(82+6−1,82).
The number of ways to put I identical items into D different cells is combin(I+D−1,I).
Think of the 100 throws as identical and the six faces of the die as different cells.
If we think in terms of going ahead and put three throws in each of the six faces, then that leaves 82 more throws that can land in any one of the six cells.
This way we have at least three of each face.