Stars and bars (combinatorics): Difference between revisions

Revision as of 07:57, 30 January 2025

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===Theorem two===

For any pair of positive integers {{mvar|n}} and {{mvar|k}}, the number of {{mvar|k}}-[[tuple]]s of '''non-negative''' integers whose sum is {{mvar|n}} is equal to the number of [[multiset]]s of size {{math|''k'' − 1}} taken from a set of size {{math|''n'' + ''k'' − 1}}, or equivalently, the number of multisets of size {{math|''n''}} taken from a set of size {{math|''k''}}, and is given by

:<math>\binom{n + k - 1}{k - 1}.</math>