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limiting combination question -- sounds easy but is it?

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limiting combination question -- sounds easy but is it? [#permalink] New post 20 Nov 2003, 08:15
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here is the question :
20 people are at the firm. 5 to be sent away on business. how many groups can be formed providing that Pres, VP and Accountant cant go altogether among 5.

Here is the way i approached it:
20-3(that cant go) = 17 than a simple combination pick 17!/(5!*12!)

here is the way Gmat Club solved it:
total number of combinations =20!/5!15!
restricting number of combinations with 3 that cant go 17!/)(2!15!)

than subctracting total minus restricted..

why cant the first method work i thought its the same?
whats the reasoning? Thanks in advance!!
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 [#permalink] New post 20 Nov 2003, 11:03
With this kind of combinatoric problems with limitations the best & the shortest way to solve is to calculate the total number of possible combinations and substract all the cases that fall under the limiting condition.

Specificaly:
a. Total number of combinations is 5C20 = 20!/ (5!15!)
b. Now imagin that you have 5 chairs, 1st, 2nd & 3rd are taken by Pres, VP and accountant respectively. You have only 4th & 5th to be taken by someone else. i.e for the 4th place we have 17 managers, for 5th place we have 16 => C(17,2) = 17!/(2!15!)
c. Total - limits = result
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Re: limiting combination question -- sounds easy but is it? [#permalink] New post 22 Nov 2003, 04:32
Leon_v wrote:
here is the question :
20 people are at the firm. 5 to be sent away on business. how many groups can be formed providing that Pres, VP and Accountant cant go altogether among 5.

Here is the way i approached it:
20-3(that cant go) = 17 than a simple combination pick 17!/(5!*12!)

here is the way Gmat Club solved it:
total number of combinations =20!/5!15!
restricting number of combinations with 3 that cant go 17!/)(2!15!)

than subctracting total minus restricted..

why cant the first method work i thought its the same?
whats the reasoning? Thanks in advance!!


This question is poorly worded. Does this mean that NONE of the 3 can go? or does this mean that any none, one, or two of the 3 can go so long as all 3 don't go?
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Vice President, Midtown NYC Investment Bank, Structured Finance IT
MFE, Haas School of Business, UC Berkeley, Class of 2005
MBA, Anderson School of Management, UCLA, Class of 1993

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 [#permalink] New post 19 Dec 2003, 16:38
I believe we need to choose 5 people to form a commitee from 20 people with the restriction that President and VP cannot be together.
This is basically
( total combinations ) - ( combinations where VP , A & P go together )

Desired combinations = 20C5 - 18C2
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 [#permalink] New post 20 Dec 2003, 05:53
I agree with AkamaiBrah that it is not clear if 2 people can go together or one alone.
  [#permalink] 20 Dec 2003, 05:53
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limiting combination question -- sounds easy but is it?

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