How many nonnegative integer solutions are there to the equa

How many non-negative integer solutions are there to the equation:

x1+x2+x3+x4 = 50

under each of the following circumstances?

a) x1 >= 1, x2 >= 1, x3 >= 1, x4 >= 1

b) At least two variables must be nonzero.

Solution

here it uses the combination with unlimited repetition :

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