A car holds seven passengers, four in the front seat and three in the back seat. How many different seating arrangements of seven people are possible if two people refuses to sit in front and one person refuses to sit in back?
A)24
B)2,520
C)864
D)6
E)1,260

Question

Quizplus · Accepted Answer

We need to first assign the seats for the people who refuse to sit in a particular section. 
Two people refuse to sit in front, leaving three people to be seated in front. This can be done in 4! = 24 ways. 
One person refuses to sit in the back, leaving six people to be seated in the back. This can be arranged in 6! = 720 ways. 
Finally, the two remaining people can be seated in the two remaining seats in 2! = 2 ways. 
Therefore, the total number of seating arrangements is 24 x 720 x 2 = 17,280. 
However, since the question only asks for the number of possible seating arrangements, we need to divide 17,280 by the number of arrangements of the people who refuse to sit in a particular section. 
This gives us a final answer of 17,280/24 = 720/1 = 864. 
Therefore, the best choice is C.

A Car Holds Seven Passengers, Four in the Front Seat