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The sandwich shop offers 8 different sandwiches. Jamey likes them all equally. He picks one randomly each day for lunch. During a given week of 5 days, let X be the number of times he chooses salami, Y the number of times he chooses falafel, and Z the number of times he chooses veggie. Find the joint probability mass function of (X,Y,Z). Identify the distribution by name.

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