In how many ways can four taxi drivers be assigned to eight cars?
A) 5,040
B) 70
C) 3,024
D) 126
E) 1,680

Question

In how many ways can four taxi drivers be assigned to eight cars? ​
A) 5,040
B) 70
C) 3,024
D) 126
E) 1,680

Quizplus · Accepted Answer

This is a combination problem, since the order in which the drivers are assigned to cars doesn't matter. We have eight choices for the first driver, seven for the second (since one car is already taken), six for the third, and five for the fourth. However, since the drivers could be assigned to the cars in any order, we have overcounted by a factor of 4! (the number of ways to order the four drivers). Therefore, the total number of assignments is:

8 × 7 × 6 × 5 / 4! = 1,680.

Therefore, the answer is (E).

In How Many Ways Can Four Taxi Drivers Be Assigned