Originally Posted by

**mtdim** Hello folks. I'm new here, but I was looking for a place where I could get some math help, as this problem has me completely stumped. It goes like this:

From the alphabet {a,b,c,d,e,f}, how many 20 letter "words" (i.e. arrangements) can be made such that no consecutive letters are the same and every letter appears at least once.

The question comes with a hint to use inclusion/exclusion, but since there are two criteria which much be satisfied, I'm not exactly sure about how to attack it this way. Should I consider each criteria separately, or do them together? Any tips would be greatly appreciated.