I'm drawing a computer-sciencey blank on how to construct a proof (I should really browse through some old textbooks.) But intuitively, the first part of the constraint (the second is redundant) says that each employee must speak a language that each other employee does not. Taken for all employees, that constraint requires one unique language per employee. 70
Each hedgie speaks 4 out of 8 possible languages.
Giving 8 C 4 = 8!/4!4! = 70 distinct possibilities.