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From a group of 8 people, it is possible to create 56 [#permalink]
18 Aug 2014, 10:24
Question Stats:
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From a group of 8 people, it is possible to create 56 different kperson committees. Which of the following could be the value of k ?
Indicate all such values. A)1 B)2 C)3 D)4 E)5 F)6 G)7




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Re: GRE Math Challenge #4 [#permalink]
04 Sep 2014, 06:58
C,E



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Re: GRE Math Challenge #4From a group of 8 people [#permalink]
03 Sep 2018, 18:00
Can someone please explain the answer?



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Re: GRE Math Challenge #4From a group of 8 people [#permalink]
03 Sep 2018, 18:31
CE is correct NixonDutt wrote: Can someone please explain the answer? Mathematically, 8 choose k = 56, therefore k=2 or 8. (Check out the formula for permutation) You could also plug in each choice below and validate it. When you're picking 2 people out of 8, the first time you have 8 choices, second you have 7, so total 8*7=56, 6 also applies because picking 6 out of 8 people for the committee is the same as picking 2 out of 8 people NOT for the committee. The other options don't make sense.
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Re: GRE Math Challenge #4From a group of 8 people [#permalink]
14 Oct 2018, 17:22
To chose k people from 8 to form 56 kperson committees:
8!/x!(8x)!= 56
I chose at random with 3, so 8!/3!5! = 8*7*6*5!/(3*2)5! = 8*7*6/6 = 56
So 3 and 5 are the answers because even when you switch 3! for 5! in the first half of the denominator, you still get the same value in the end.
I hope that makes sense!



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From a group of 8 people, it is possible to create exactly 5 [#permalink]
11 Dec 2018, 14:17
From a group of 8 people, it is possible to create exactly 56 different kperson committees. Which of the following could be the value of k? Indicate all such values. A. 1 B. 2 C. 3 D. 4 E. 5 F. 6 G. 7
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Re: From a group of 8 people, it is possible to create exactly 5 [#permalink]
12 Dec 2018, 09:36
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Carcass wrote: From a group of 8 people, it is possible to create exactly 56 different kperson committees. Which of the following could be the value of k?
Indicate all such values.
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7 Explanation::As, 56 different k  committee can be formed by the group of 8 people, that means 8Ck = 56 Now it is require to check the value of k from the option which results to 56 When K= 5,\(8C5 = \frac{(8*7*6*5!)}{(5!*3!)} = 56\) When K= 3,\(8C3 = \frac{(8*7*6*5!)}{(5!*3!)} = 56\)
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Re: From a group of 8 people, it is possible to create exactly 5 [#permalink]
09 Jan 2019, 01:48
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we know this is Combination based, and order doesnt matter, so we have
8cK=56
8!/(k!*(8k!)=56
lets ditch the fraction
8!= 56(k!*8k)! divide 8! by 56 (which is 8*7) and we have 6! =(k!*8k)! 720 =(k!*8k)!
Dont bother plugging in 1, since that will give you a multiple of 7, and that cant make 720, try pluggin in 2
720=(2!*6!) ===nope 2!*6!= 1440 work your way up
720=(3!*5!) that works
try k=4
720= 4!*4!.. nope, that equals 576
try k =5
720=5!*3!, which is identical to k=3
try k=6
720= 6!*2!... nope
you cant go higher than that, it wont make sense.
The answers are C and E



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Re: From a group of 8 people, it is possible to create exactly 5 [#permalink]
09 Jan 2019, 06:20
Carcass wrote: From a group of 8 people, it is possible to create exactly 56 different kperson committees. Which of the following could be the value of k?
Indicate all such values.
A. 1
B. 2
C. 3
D. 4
E. 5
F. 6
G. 7 So, 8Ck = 56 = 8*7... You can substitute k as 2 and see.. 8C2=\(\frac{8*7}{2}\), so take k as 3 8C3=\(\frac{8*7*6}{3!}=56\), so 3 is one value.. Also 8Ck = 8C(8k).....if k is 3, 8k=83=5.. Thus 3 and 5 are the answers. otherwise \(8Ck=56...\frac{8*7*6!}{(8k)!k!}=56.....\frac{6!}{(8k)!k!}=1....6!=(8k)!k!....6*5!=(8k)!k!....3!5!=(8k)!k!\) Thus, k can be 3 or 5.
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Some useful Theory. 1. Arithmetic and Geometric progressions : https://greprepclub.com/forum/progressionsarithmeticgeometricandharmonic11574.html#p27048 2. Effect of Arithmetic Operations on fraction : https://greprepclub.com/forum/effectsofarithmeticoperationsonfractions11573.html?sid=d570445335a783891cd4d48a17db9825 3. Remainders : https://greprepclub.com/forum/remainderswhatyoushouldknow11524.html 4. Number properties : https://greprepclub.com/forum/numberpropertyallyourequire11518.html 5. Absolute Modulus and Inequalities : https://greprepclub.com/forum/absolutemodulusabetterunderstanding11281.html



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Re: From a group of 8 people, it is possible to create 56 [#permalink]
16 Dec 2019, 12:12
Bump for further discussion
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Re: From a group of 8 people, it is possible to create exactly 5 [#permalink]
01 May 2020, 02:54
One important doubt here, it says 56 different groups, but it does not say that there CAN ONLY BE 56 groups. So even if we take 4 people out of 8 (where it's the maximum number of configurations possible), we CAN TAKE 56 different groups from this list. So shouldn't 4 be included as well?



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Re: From a group of 8 people, it is possible to create exactly 5 [#permalink]
01 May 2020, 12:39
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Zohair123 wrote: One important doubt here, it says 56 different groups, but it does not say that there CAN ONLY BE 56 groups. So even if we take 4 people out of 8 (where it's the maximum number of configurations possible), we CAN TAKE 56 different groups from this list. So shouldn't 4 be included as well? Great question!! Many students have posed very similar questions. For example, if a question tells us that A woman owns 5 dogs, must we assume that she has exactly 5 dogs? After all, she could have 6 dogs, since it would still be true that there are 5 dogs in her possession (plus 1 more). If this were the accepted standard, it would be next to impossible to phrase questions that are free from ambiguity. So, on the GRE, if you're told that there are X things, we can assume that there are exactly X things. So, for the question above, we can assume that there are exactly 56 different kperson committees possible. If the author intended to phrase the question as you are suggesting, it would read something like " From a group of 8 people, we can create AT LEAST 56 different kperson committees. Which of the following could be the value of k?" Cheers, Brent
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Re: From a group of 8 people, it is possible to create exactly 5
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01 May 2020, 12:39





