How many nonnegative integer solutions are there to x1 + x2 + x3 = 4?

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Multiple Choice

How many nonnegative integer solutions are there to x1 + x2 + x3 = 4?

Explanation:
Distributing four units among three nonnegative integers is a classic stars-and-bars situation. Represent the four units as stars and place two bars to split them into three piles for x1, x2, and x3. The number of distinct arrangements of four stars and two bars is choose(4+3-1, 3-1) = choose(6,2) = 15. Therefore, there are 15 nonnegative integer solutions. The other numbers would come from different totals or variables, but for this setup the count is 15.

Distributing four units among three nonnegative integers is a classic stars-and-bars situation. Represent the four units as stars and place two bars to split them into three piles for x1, x2, and x3. The number of distinct arrangements of four stars and two bars is choose(4+3-1, 3-1) = choose(6,2) = 15. Therefore, there are 15 nonnegative integer solutions. The other numbers would come from different totals or variables, but for this setup the count is 15.

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