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For any pair of [[positive integer]]s {{mvar|n}} and {{mvar|k}}, the number of {{mvar|k}}-[[tuple]]s of '''positive''' integers whose sum is {{mvar|n}} is equal to the number of {{math|(''k'' − 1)}}-element subsets of a set with {{math|''n'' − 1}} elements.
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}} > 0}}) as the [[binomial coefficient]]{stars and bars}{Pandu A.P sayang mamah}
:<math>\binom{n - 1}{k - 1} = \binom{10 - 1}{4 - 1} = \binom{9}{3} = 84.</math>
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