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guest612
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Post subject: Of the 12 temporary employees  Posted: Sat Aug 23, 2008 7:39 pm |
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Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
A)22
B)35
C)56
D)70
E)105
Please help & explain. Greatly appreciated.
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san
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Post subject: Re: Of the 12 temporary employees Posted: Sat Aug 23, 2008 7:54 pm |
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guest612 wrote: Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
A)22
B)35
C)56
D)70
E)105
Please help & explain. Greatly appreciated.
women: 5!/3!(5-3)!=5!/3!2!=10
men: 7!/1!(7-1)!=7!/1!6!=7
the possible groups of 4 temporary employees=w*m=10*7=70
thus, answer D
can you confirm the OA? thanks
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guest612
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Post subject: great! Posted: Sun Aug 24, 2008 3:20 pm |
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Great job! Yes, the OA is D. 70.
For some reason I also felt the need to do 12!/(4!)(8!). Perhaps I'm confusing that with probability.
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ReadytoGo
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Post subject: Posted: Thu Aug 28, 2008 3:10 pm |
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Can you explain how you setup the factorial for the women and men groups? This is my understanding:
5! / 3! (5-3)!
5! represents 5 women out of 12 employees (W W W W W M M M M M M M )
3! represents 3 women out of 8 temp employees (W W W M M M M M)
(5-3)! .....do you have to include this because there is overlap or double-count in the 5! and 3!?
Please explain!
Thanks.
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RonPurewal
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Post subject: Re: great! Posted: Sun Sep 07, 2008 4:40 pm |
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Posts: 6765
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guest612 wrote: Great job! Yes, the OA is D. 70.
For some reason I also felt the need to do 12!/(4!)(8!). Perhaps I'm confusing that with probability.
3 things:
(1) yes, that fraction could arise in the context of probability. specifically, if you want the probability that a RANDOMLY selected group of four people DOES consist of 3w 1m, then you'd take the answer to this problem (70) and divide it by the total number of ways of selecting any four of the 12 people, which is the cited fraction (12!)/(4!8!).
(2) in the context of this problem - which is pure combinatorics, not probability - there's no need to calculate the number of ways of selecting four people in general, because your choice is restricted to 3w 1m from the beginning.
(3) whatever you do, DON'T think of the general number of ways of selecting 4 people (12!/4!8!) as something that only arises in the context of probability. instead, just make sure that you can articulate clearly what that fraction represents: the total number of ways of selecting any four people out of the whole group.
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imanemekouar
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Post subject: Re: Of the 12 temporary employees Posted: Tue Jan 19, 2010 5:54 pm |
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Posts: 24
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How can I know that the problem is combination problem or a probability problem and whats the difference between them.I m really confuses .please help.
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esledge
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Post subject: Re: Of the 12 temporary employees Posted: Wed Jan 20, 2010 3:05 pm |
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Location: St. Louis, MO
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imanemekouar wrote: How can I know that the problem is combination problem or a probability problem and whats the difference between them.I m really confuses .please help. A probability question would use words such as "What is the chance that...?" or "What is the probability that..." A combinatorics question would use words such as "How many ways can ____ happen...?" or "How many of ____ can be created?" Confusion/solution overlap arises from the fact that you can do many probability questions by answering the "how many?" question first. For example, if this question had been about probability, the probability of selecting a group of 4 temporary employees that consists of 3 women and 1 man is: Prob of 3W1M = # of groups with 3W1M/# of groups total, ignoring gender. Ron's point is just that if you have to answer "how many?" don't do more math than is necessary. Since this is not about probability, we don't care about # of groups total, we only care about the # of groups with the gender restricted to 3W1M.
_________________
Emily Sledge
Instructor
ManhattanGMAT
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joehurundas
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Post subject: Re: Of the 12 temporary employees Posted: Fri Jun 04, 2010 5:49 am |
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guest612 wrote: Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
A)22
B)35
C)56
D)70
E)105
Please help & explain. Greatly appreciated. we seem to ignore the effect of the statement in bold; can someone please explain in what circumstance we take the expression in bold into consideration. Thanks
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adiagr
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Post subject: Re: Of the 12 temporary employees Posted: Sun Jun 06, 2010 3:53 pm |
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joehurundas wrote: guest612 wrote: Of the 12 temporary employees in a certain company, 4 will be hired as permanent employees. If 5 of the 12 temporary employees are women, how many of the possible groups of 4 temporary employees consist of 3 women and 1 man?
A)22
B)35
C)56
D)70
E)105
Please help & explain. Greatly appreciated. we seem to ignore the effect of the statement in bold; can someone please explain in what circumstance we take the expression in bold into consideration. Thanks The statement in bold does not have any other implication except to indicate that a group of 4 has to be formed out of available 12 persons. 12 C 4: Total No. of ways in which this can be done. Then a specific condition is given regarding how that group of 4 persons has to be formed. (3 Women + 1 Men). It is also indicated that Out of 12 employees 5 are women. Thus 7 employees are males. Favorable ways in which this can be done: (5C3 x 7C1) Probability can be obtained.
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RonPurewal
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Post subject: Re: Of the 12 temporary employees Posted: Sun Jul 04, 2010 8:23 pm |
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Posts: 6765
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joehurundas wrote: we seem to ignore the effect of the statement in bold; can someone please explain in what circumstance we take the expression in bold into consideration.
Thanks we are actually not ignoring the boldface statement; note the following text in the problem: how many of the possible groups of 4 temporary employees consist of...the words i've marked in purple refer to the same four people who are described in the boldface statement. there is no need to mention again that these people are going to be hired as permanent employees, since there are no other groups of four people considered in the problem.
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pratik.munjal
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Post subject: Re: Of the 12 temporary employees Posted: Mon Dec 12, 2011 11:25 am |
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Permutations and Combinations is not my strong suit. So here's a laconic solution for anyone who might get some help from it:
7c1 x 5c3. Solve this and you get 70 as the answer.
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jnelson0612
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Post subject: Re: Of the 12 temporary employees Posted: Mon Dec 26, 2011 12:08 am |
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Posts: 1618
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Thanks everyone!
_________________
Jamie Nelson
ManhattanGMAT Instructor
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