Determine the number of ways of selecting 2 teachers from 19 ones; one is to train some students in mathematics, and the other is to prepare their test.
Firstly, we consider the number of possible options for the teacher who will teach the mathematics class. Since there are 19 teachers, there are 19 options.
This leaves 18 possible options for writing the exam. Hence, the number of ways of selecting the two teachers is .