Eight gentlemen check their hats at a restaurant. a) In how many ways can the hats be returned at random? b) What is the probability that no one recieves his own hat? c) Determine the same probability for nine and ten gentlemen d) For eight, nine, or ten gentlemen when is the probability greatest that no one recieves his own hat?   I think the answer to part (a) is 8! but I am not sure. The book only gives the answer to part (d) and it is that P(8) is the greatest. I am mainly stuck on parts (b) and (c). Thanks!

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