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Refer to Example 2.13. Suppose that the number of distributors is M = 10 and that there are n = 7 orders to be placed. What is the probability that
a all of the orders go to different distributors?
*b distributor I gets exactly two orders and distributor II gets exactly three orders?
*c distributors I, II, and III get exactly two, three, and one order(s), respectively?
EXAMPLE 2.13 A company orders supplies from M distributors and wishes to place n orders (n < M). Assume that the company places the orders in a manner that allows every distributor an equal chance of obtaining any one order and there is no restriction on the number of orders that can be placed with any distributor. Find the probability that a particular distributor—say, distributor I—gets exactly k orders (k ≤ n).
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Mathematical Statistics with Applications
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