My son is doing a math worksheet. He is practicing the concept of 'carrying' when doing sums. The sheet has 16 problems, each is summing two three-digit numbers. What struck me as interesting was that the creator of the problems made every problem have at least two carries and most have three.

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What is the probability distribution for the number of carries in finding the sum of two randomly selected three-digit numbers?
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Feel free to generalize.