n guys are collecting one hat and one umbrella from the valet.

a) In how many ways the valet can bring them back their stuff such that nobody will get both the hat and the umbrella (but they can get one of them).

b) In how many ways the valet can bring them back their stuff such that nobody will get their hat or the umbrella (or both)?

I've tried to solve this problem with the inclusion-exclusion prinicple, but i didn't succeed.

Thanks for any kind of help