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Stars and Bars or "Balls and Urns": Multichoose Coefficients

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Explanations 1

See here.
By Benjamin Qi

Problems 1

The number of arrangements of a standard 52-card deck can be expressed in the form a⋅b!,a\cdot b!,a⋅b!, where aaa and bbb are integers such that bbb is as large as possible. Com…