Problem: 7 swimmers are participating in a swimming match; 3 Americans, 2 Germans, 1 Australien and 1 Dutch. The swimming tracks 1 till 7 are randomly assigned.

Two questions:

1) What is the chance that 1 of the Germans is swimming in a outer track (so that would mean 1 german in track 1 or track 7)

2) What is the chance that at least 1 of the non-Americans is swimming in a outer track?

Could somebody please tell me how to calculate this?

I think I should divide the number of succesful outcomes by the total number of outcomes.

Total number = 7! = 5040

But how do I find the number of succesful outcomes in this case...

Answers should be

1) 0.476

2) 0.857