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.

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* 24* 24=9216\ ways`

Hence, there are 9216 different ways.