Question #3cd19

1 Answer
Oct 20, 2016

210 ways

Explanation:

You start by placing Alice, there are 3 ways. then there are are 2 ways of placing Jack. So we have 6 ways of placing Alice and Jack.
In the car with Alice, there are ¹C=10!7!3!=1098123=120 ways for the first car.

For the second car, you may or may not have Jack.
If Jack is in the second car, there are C=7!4!3!=765123=35 ways for the second car.

For the third car, there is 1 way.
If Jack is not in the third car, then we have C=7!3!4!=35 ways for the second car and 1 way for the third car.

Putting it all together =6(35)=210 ways