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stat question A scientist has 15 books: 3 books in each of her 5 favorite topics. She places the books on a shelf uniformly at

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A scientist has 15 books: 3 books in each of her 5 favorite topics. She places the books on a shelf uniformly at random. (a) What is the probability that the 3 books in her favorite topic are placed next to each other? Let X be the number of topics whose books are placed next to each other. (b) Prove that the expectation of X is equal to 1/7. (c) What is the probability that X = 0

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