Question: 4. (Total: 10 points) Suppose 7 identical balls are randomly thrown into 5 distinct empty boxes where each box can take up to 9 balls.

4. (Total: 10 points) Suppose 7 identical balls are randomly thrown

4. (Total: 10 points) Suppose 7 identical balls are randomly thrown into 5 distinct empty boxes where each box can take up to 9 balls. (a) (2 points) How many different patterns are there in total? 330 (b) (1 point) How many patterns are there such that exactly 1 box is empty? 120 (c) (3 points) How many patterns are there such that exactly 2 boxes are empty? B6 (d) (4 points) What is the probability that exactly 2 boxes are empty? 556

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