SAT question :)......?

Question

...

The Acme Plumbing Company will send a team of 3 plumbers to work on a certain job. The company has 4 experienced and 4 trainees. If a team consists of 1 experieced plumber and 2 trainees, how many different such teams are possible?

i thought first it could be any of the 4 experienced
then any of the 4 trainees
then any of the 3 trainees left

...so
4 x 4 x 3 = 48

but the ****answer is 24****
...where did the (divided by 2) come from

Answer 1

It comes from the trainees. Let's say you you have trainees A, B, C, and D. You can pick trainee A first and then trainee B next. You can also pick trainee B first and then trainee A. This shows that we are counting the trainees twice, so we must half the result.



Another way to do it is note that there are C(4, 2) = 6 ways to pick the trainees and 4 ways to pick an experienced person. Thus, there are 6*4 = 24 ways to pick the members of the team.



I hope this helps!

Answer 2

4 x 3 x 2= 24

Answer 3

Use a TI-83 calculator and input 4C3 + (or times, I can't remember) 4C2.



This is the combination formula thingy. Make sure you put in C and not P.

Answer 4

4C3 = 24 (do it on any calculator),