A group of 12 people want to go to a concert. They can travel in a small car that takes one driver and one passenger and two cars each taking one driver and 4 passengers. If there are five drivers in the group, in how many different ways can they travel.
What I did: There are 5C3 ways I can choose the drivers and then 3 ways that I can arrange them into the cars (i.e. I'm deciding who drives the small car and the rest is forced).
There are then 9 ways I can choose who the passenger is in the small car and then 8C4 ways to divide the remaining passengers into 2 groups of 4. This yields and answer of 18900 ways and yet the given answer is 6300 ways. What am I doing wrong?
Correct me if I'm wrong (I'm new to this) but I think the correct answer is 6300:
12 total people
You have 5 drivers and 3 cars (5C3) you take 3 people, so you're left with 9 people
One of the cars supports one passenger (9C1) you take 1 person, now 8 people are left
The other car supports 4 passengers (8C4) so you're left with 4 people that automatically go into the other car that supports 4 passengers
So (5C3) * (9C1) * (8C4)=6300