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:



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.
2.
3.

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