Stars and Bars (Probability)
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the context of combinatorial mathematics, stars and bars refers to a trick used to derive certain combinatorial theorems.Suppose one has k objects (to be represented as stars; in the example below k = 7) to be placed into n bins (in the example n = 3), such that all bins contain at least one object; one distinguishes the bins (say they are numbered 1 to n) but one does not wish to distinguish the k stars (so configurations are only distinguished by the number of st...
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In the context of combinatorial mathematics, stars and bars refers to a trick used to derive certain combinatorial theorems.Suppose one has k objects (to be represented as stars; in the example below k = 7) to be placed into n bins (in the example n = 3), such that all bins contain at least one object; one distinguishes the bins (say they are numbered 1 to n) but one does not wish to distinguish the k stars (so configurations are only distinguished by the number of stars present in each bin; in fact a configuration is represented by a n-tuple of positive integers as in the statement of the theorem).
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