The number of ways of accomodating 7 guests in 3 rooms so thst no room is empty is

a)1260 b)1440 c)1708 d)1806

3^7 - 3*2^7 + 3*1^7 = 2187 - 384 + 3 = 1806

Inclusion-Exclusion principle.

7 guests go into 3 rooms (1 and 2 rooms can be empty) - 7 guests go into 2 rooms (1 and 2 rooms can be empty) + 7 guests go into 1 room (This was excluded twice)