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A distribution center receives shipments of a product from 3 different factories in the following quantities: 50, 35, and 25. Three times a product is

A distribution center receives shipments of a product from 3 different factories in the following quantities: 50, 35, and 25. Three times a product is selected at random, each time without replacement. Find the probability that

(a) all three products came from the third factory and

(b) none of the three products came from the third factory.

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