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28 December, 05:58

Solutions to equations involving a sum of integer valued variables. About (a) How many solutions are there to the equation where each is a non-negative integer

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  1. 28 December, 06:31
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    I think your question is missing something, i tried to explain you by examples.

    Explanation:

    1)

    n = 37, k = 6.

    Thus, the answer is (37 + 6 - 1) C6-1 = 42C5

    => C (42,5) = 850668

    Where C (n, r) is the combination

    2)

    n = 37

    Since xi > = 2 that means x1 > = 2, x2 > = 2, x3 > = 2, x4 > = 2, x5 > = 2, x6 > = 2

    Then, we distribute the remaining 37 - 2 - 2 - 2 - 2 - 2 - 2 = 25

    Thus, the answer is (25 + 6 - 1) C6-1 = 30C5

    => C (30,5) = 142506
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