C(4,2)*2! *5!
Total =7! -C(4,2)*2! *5! =5040- 1440=3600
When you see "at least", it is easier to do it by exclusion.
There is something wrong with the second method. When A is the monitor, it includes the case that B is the vice monitor, and then when you consider B, it also includes the case that A is the monitor. repetitive computation