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How many positive integral solutions are there for the equation x + y + z + w = 20?

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How many positive integral solutions are there for the equation x + y + z + w = 20 ?

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The number of positive integral solutions of the given equation is equal to number of ways to divide 20 identical objects among 4 persons such that each gets one or more. Therefore, the total number of solutions is

19C3 (n - 1Cr - 1) = 969

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