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Do each of the following: a) How many integer solutions to x 1 + x 2...

Do each of the following:

a) How many integer solutions to x 1 + x 2 + x 3 + x 4 + x 5 + x 6 = 35 are there if all of x 1through x 6are nonnegative?

b) How many integer solutions to x 1 + x 2 + x 3 + x 4 + x 5 + x 6 = 35 are there if x 1 ≥ 5, x 2 ≥ 1, x 3 ≥ 2 and all the other variables are nonnegative?

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