You are sorting assigning 6 people, A, B, C, D, E and F, into 3 different hotel rooms. How many ways can they be sorted such that A is in the same room with C, and B is not in the same room with D? (Some hotel rooms may be empty.)
7C5 * 2! * 5! - 6C4 * 2! * 2! *4!
=5040-1440
=3600