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22 Jan 2021, 01:15
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Difficulty:
95%
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Question Stats:
39% (02:02) correct
61%
(02:07)
wrong
based on 76
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The New Oxnard Resort and Spa will hire 12 individuals to fill the positions of greeter, janitor, consultant, fry cook, and massage therapist. If each individual will be hired for 2 positions, and no position will be filled by more than 9 individuals, how many distinct groups of individuals could be hired as greeters?
(1) 66 distinct groups each of massage therapists, fry cooks and consultants could be hired.
(2) All of the fry cooks are also hired as consultants and all of the janitors are also hired as greeters.
Are You Up For the Challenge: 700 Level Questions
(1) 66 distinct groups each of massage therapists, fry cooks and consultants could be hired.
(2) All of the fry cooks are also hired as consultants and all of the janitors are also hired as greeters.
Are You Up For the Challenge: 700 Level Questions
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22 Jan 2021, 19:09
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Bunuel
There are two ways to understand this allocation, each person picks 2 out of the 5 occupations (given the hiring constraints) and we aggregate every person's picks to get 24 positions in total. Or we have 24 positions in total, and the 12 applicants fill in 2 different positions each.
Statement 1:
Note \(12C2 = \frac{12*11}{2!} = 66\) (we also have 12C10 = 66 but we can't choose 10 people for any position). Therefore the 66 distinct groups means we are hiring 2 people for massage therapists, fry cooks, and consultants each. Note however there are 24 positions in total we consider. Thus there are 18 positions left for greeters and janitors. Since no position will be filled by more than 9 individuals, we must have 9 of each. Thus there are 12C9 possible groups for janitors and greeters. Sufficient.
Statement 2:
We have this relation of consultants containing cooks, and greeters containing janitors. However, we are still missing a lot of information, such as info on massage therapists, or the number of cooks/janitors etc. Insufficient.
IMO A
I think the question may have a flaw when combining the statements however, combining the information we can conclude all massage therapists much also be hired as a consultant or greeter. We know there cannot be any MT's + consultants due to statement 1 having Fry Cook = Consultant = 2, thus all MT's must also be greeters. Yet we have Janitors = Greeters = 9 so there is a contradiction.
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21 Aug 2023, 18:54
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Bunuel can you help with the solution here please?
