Tom and Jim are distant cousins who meet during their family Thanksgiving meal. Tom tells Jim that he has 3 kids, and the product of their ages is 72. He also tells him the sum of their ages. Jim says he still can’t correctly guess the ages of Tom's kids. Finally, Tom says, "My youngest child's name is Joy." Jim can then correctly guess. What are the ages?

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How many combinations of 3 numbers can you come up with whose product is 72? What are they?

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