## Train car: probability to have a seat

A train has got five train cars, each one with N seats. There are 150 passengers who randomly choose one of the cars. What is the probability that everyone will get a seat?

I think that what is asking me is "what is the probability that each wagon is chosen by no more than N passengers"?

The probability of having people in *a* wagon is given by
.

I thought of the answer being .. but I think that the events

- wagon a is chosen by no more than N passengers
- wagon b is chosen by no more than N passengers
- wagon c is chosen by no more than N passengers
- wagon d is chosen by no more than N passengers
- wagon e is chosen by no more than N passengers

are far from being independent... So what could I do?
Thanks a lot