How many ways can 14 people fit in three cars, two with 4 seats and one with 3

Say everyone goes to a football game. What is the probability that the three car owners will sit together?

4 4 3

Order is not important, so the total number of ways of fitting 14 people would be:

14C4\ \times\ 10C4\ \times\ 6C3

There are three 'general' ways that they can sit together:
1. All three go into the car with 3 seats.
2. All three go into a car with 4 seats.
3. All three go into the last car with 4 seats.

1. 3C3\ \times\ 11C4\ \times\ 7C3
2. 3C3\ \times\ 11C1\ \times\ 10C4\ \times\ 6C3
3. 3C3\ \times\ 11C1\ \times\ 10C4\ \times\ 6C3

Add 1, 2 and 3 and divide by the initial part to get the probability.