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

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(52776) (Show Source): You can put this solution on YOUR website!
.


 = 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

RELATED QUESTIONS
their are six people getting on a bus, there are 8 seats, how many different... (answered by stanbon)

if there is 8 empty seats on a bus and 5 people get on how many possible ways can they be (answered by mathmate)

Problem 3.10. How many ways are there to seat 8 people, consisting of 4 couples, in a row (answered by jim_thompson5910)

There are 6 boys who enter a boat with 8 seats, 4 on each side. In how many ways can they (answered by ikleyn)

How many different ways can four people be seated on a bench that seats... (answered by scott8148)

In how many ways can 7 people seated on a sofa if there are only 4 seats available? (answered by reviewermath)

How many ways can 4 people arrange themselves inside a van that has 10... (answered by EdenWolf)

How many ways can 4 people arrange themselves inside a van that has 6... (answered by EdenWolf)

How many different ways can 4 people be seated in a row of 4 seats? (answered by jim_thompson5910)