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# help probability

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Miyu is giving out 9 identical chocolates to her 7 friends, including Dhruv.  All possible distributions are equally likely.  What is the probability that Dhruv gets exactly 2 chocolates?

Dec 14, 2022

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9 chocolates, 7 friends = 9 stars, 6 bars. So, there are $${15 \choose 6} = 5005$$ combinations.

If Dhruv gets 2, there are 5 chocolates for 6 people, which means there are 7 stars and 5 bars, making for $${12 \choose 5} = 792$$ cases

So, the probabilty is $${792 \over 5005} = \color{brown}\boxed{72 \over 455}$$

Dec 14, 2022