1. First, choose one person and choose the method of 5*6, then the second person has 4*5=20 methods, and the rest have 3*4. Because the people chosen are in no order, a total of 6 * 5 * 5 * 4 * 3/3! = 1200 selection method.

2. If A goes, B can't go, C must go, and the remaining three places will be chosen randomly among the remaining five teachers. There are C53 ways to choose from.

A doesn't go, C doesn't go, B doesn't care. At this time, there are four places among the six teachers except A and C, and there are C64 ways to choose from.

So there are always * * * C53+C64=25 options.