A group of fifteen tourists is stranded in a city with four hotels of the same class. Each of the hotels has enough room available to accommodate the fifteen tourists. The group's guide, who has a good working relationship with each of the four hotels, assigns the tourists to the hotels as follows. First, he randomly determines how many are to go to hotel A, then how many of the remaining tourists are to go to hotel B, and then how many are to go to hotel C. All remaining tourists are sent to hotel D. Note that each stage of the assignment the guide draws at random a number between zero and the number of tourists left. What is the probability that all four hotels receive guests from the group?
A group of fifteen tourists is stranded in a city with four hotels of the same class. Each of the hotels has enough room available to accommodate the fifteen tourists. The group's guide, who has a good working relationship with each of the four hotels, assigns the tourists to the hotels as follows. First, he randomly determines how many are to go to hotel A, then how many of the remaining tourists are to go to hotel B, and then how many are to go to hotel C. All remaining tourists are sent to hotel D. Note that each stage of the assignment the guide draws at random a number between zero and the number of tourists left. What is the probability that all four hotels receive guests from the group?
Chapter8: Sequences, Series,and Probability
Section8.6: Counting Principles
Problem 5ECP: How many permutations of the letters W, X, Y, and Z are possible?
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Transcribed Image Text:A group of fifteen tourists is stranded in a city with four hotels of
the same class. Each of the hotels has enough room available to accommodate
the fifteen tourists. The group's guide, who has a good working relationship
with each of the four hotels, assigns the tourists to the hotels as follows. First,
he randomly determines how many are to go to hotel A, then how many of
the remaining tourists are to go to hotel B, and then how many are to go to
hotel C. All remaining tourists are sent to hotel D. Note that each stage of the
assignment the guide draws at random a number between zero and the number
of tourists left. What is the probability that all four hotels receive guests from
the group?
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