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!

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!

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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Question

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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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