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Will Orrick (talk | contribs) Undid revision 1261503615 by 50.100.205.138 (talk) It was correct before. These parameters are what you get if you interchange the roles of bars and stars. |
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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 [[cardinality]] {{math|''n''}} taken from a set of size {{math|''k''}}, or equivalently, the number of multisets of cardinality {{math|''
For example, if {{math|1=''n'' = 10}} and {{math|1=''k'' = 4}}, the theorem gives the number of solutions to {{math|1=''x''{{sub|1}} + ''x''{{sub|2}} + ''x''{{sub|3}} + ''x''{{sub|4}} = 10}} (with {{math|''x''{{sub|1}}, ''x''{{sub|2}}, ''x''{{sub|3}}, ''x''{{sub|4}} <math>\ge0</math> }}) as:
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