SOLUTION: 4 couples (8 people) are getting on a double-decker bus that has 4 seats on each floor. How many different ways can they sit on the bus so that each person's partner is on the oppo
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-> SOLUTION: 4 couples (8 people) are getting on a double-decker bus that has 4 seats on each floor. How many different ways can they sit on the bus so that each person's partner is on the oppo
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Question 1156986: 4 couples (8 people) are getting on a double-decker bus that has 4 seats on each floor. How many different ways can they sit on the bus so that each person's partner is on the opposite floor?
My try was 2 ways to select the floor.
2 ways to select a person from each couple. So 2^4 = 16 ways to select a person from all the 4 couples.
Also to arrange 4 persons on the top floor 4! and to arrange 4 persons on the bottom floor 4!.
So 2 * 2^4 * 4! * 4! = 18432 ways. Answer by ikleyn(52775) (Show Source):
= 16 ways to select a person from each and all the 4 couples,
to send him (or her) to the upper deck.
4! = 24 ways to order people on the bottom floor.
4! = 24 ways to order people on the upper floor.
In all, 16 * 24 * 24 = 9216 ways. ANSWER
