15. The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced plumbers and 4 trainees. If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?My friend Debbie Stier got it right -- ! After she explained it to me, C. and I saw what we were doing wrong (double-counting the trainee pairs, basically), too, but we wanted to watch the Khan video to see how he did it.
Turns out Salman Khan did the problem the same way C. and I did.
Which makes me feel somewhat better.
Best explanation for novices on College Confidential:
Best way to approach this:
Fact 1: There are 4 different experienced plumbers.
Fact 2: There are 6 different combinations of 2 trainees in a total group of 4 trainees. If this isn't obvious, let the 4 trainees be A, B, C, and D.
All the possible trainee pairs:
AB, AC, AD
and each of these trainee pairs can go with any of the 4 experienced plumbers, so we multiply 6 X 4 for the total number of possible teams, which gives 24. A common error here would be to erroneously consider AB a different pair from BA, when really order doesn't matter in this problem. That is how you would get a wrong answer of 48.