Question

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?

Answer 1

Answer: There are 9216 different ways.

Step-by-step explanation:

Since we have given that

Number of couples = 4

Number of people in couples = 8

Number of seats on each floor = 4

Number of ways to select a person from each to send him (or her) to the upper deck would be

$2^4=16\ ways$

Number of ways to select a person to send them to the bottom floor would be

$4!=24$

Number of ways to select a person to send them to the upper floor would be :

$4!=24\ ways$

So, the total number of different ways would be :

$16\times 24\times 24=9216\ ways$

Hence, there are 9216 different ways.