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Blue Book: Math, pg. 657, #15

tux08902tux08902 1015 replies121 threadsRegistered User Senior Member
edited August 2007 in SAT Preparation
Guys, I need help with this question. I just can't figure out how the answer can be 24.
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?

"If a team consists of 1 experienced plumber and 2 trainees, how many different such teams are possible?"

So, that would mean 4 plumbers x 4 trainees x 3 trainees (1 picked already), which would mean 48. Now, how is it 24 and not 48?
edited August 2007
6 replies
Post edited by tux08902 on
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Replies to: Blue Book: Math, pg. 657, #15

  • pickpick 219 replies18 threadsRegistered User Junior Member
    The order doesn't matter in this question, so you're doing it wrong by using permutation for the trainees--permutation counts the order.

    You have to use combination... 4C1 x 4C2 = 4 x 4x3/2 = 24

    In your method, exp + trainee + trainee and trainee + trainee + exp count as different teams, but they're the same.
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  • tux08902tux08902 1015 replies121 threadsRegistered User Senior Member
    Wow, I just realized that. Thanks for the explanation. I have to start being more careful on this stuff.
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  • pickpick 219 replies18 threadsRegistered User Junior Member
    Yeah, this kind of stuff confuses me as well.

    Just to make sure though, how would one calculate this if the order mattered?

    So 24 teams are possible.... then you do permutation for 3?

    24 x 3! which equals 144. Can anyone verify this?
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  • akahmedakahmed 857 replies98 threads- Member
    Since order does not matter, because one plumber is the same as another and one trainee is the same as another trainee, you first

    Find all possible combinations of 2 trainees out of 4 possible , so in calc
    4 nCr 2 = 6
    Then you need one out of 4 plumbers at a time, so there are 4 possibilities
    4 nCr 1 = 4

    6 x 4 = 24
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  • E-A-S-EE-A-S-E 80 replies13 threadsRegistered User Junior Member
    I did it the long way didnt take me that long..
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  • chrisiskeychrisiskey 181 replies5 threadsRegistered User Junior Member
    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?

    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
    BC,BD
    CD

    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.
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