I'm going to number the 4 experienced plumbers 1, 2, 3, and 4, and then the trainees 5, 6, 7, and 8. Then I'm just going to follow the instructions in the problem (1 experienced plumber and 2 trainees) and see if I can recognize the pattern that emerges before I count up every combination.
Start with experienced plumber #1. He can be accompanied by the following sets of trainees:
5, 6
5, 7
5, 8
6, 7
6, 8
7, 8
Remember, "5, 6" is the same as "6, 5" in this question, since in both cases trainees 5 and 6 will be accompanying experienced plumber 1.
OK, now what trainees can accompany experienced plumber #2?
5, 6
5, 7
5, 8
6, 7
6, 8
7, 8
The SAME ONES. Once we see the pattern, we don't need to finish listing. There are 6 possible combinations of trainees for each of 4 experienced plumbers. (6)(4) = 24. That's 24 possible combinations.
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