SOLUTION: There are 4 hotels in a certain city. If 3 men check into hotels in a day, find the probability that each check into (i) a different hotel & (ii) the same hotel.

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Question 745070: There are 4 hotels in a certain city. If 3 men check into hotels in a day, find the probability that each check into (i) a different hotel &
(ii) the same hotel.

Answer by sachi(548) (Show Source):
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There are 4 hotels in a certain city. If 3 men check into hotels in a day,
the probability that each check into (i) a different hotel
the 1st man enters into a hotel 1n 4 ways
the 2nd man enters into a hotel 1n 3 ways (as one hotel is booked )
the 3rd man enters into a hotel 1n 2 ways (as two hotel is booked )
so the probability =4*3*2=24
the probability that each check into (ii) the same hotel.
the 1st man enters into a hotel 1n 4 ways
the 2nd man enters into a hotel 1n 4 ways (as hotel is repeated )
the 3rd man enters into a hotel 1n 4 ways (as hotel is repeated)
so the probability =4*4*4=64