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# 1- In how many ways can seven vacancies at a company be

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Intern
Joined: 30 Oct 2004
Posts: 5

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1- In how many ways can seven vacancies at a company be [#permalink]

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10 Nov 2004, 20:47
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

1- In how many ways can seven vacancies at a company be filled if there are 20 job applicants, three of the vacancies are identical secretarial positions and the remaining four are identical sales representative positions? Assume that all 20 applicants have applied for all seven positions.

A. 20Â·19Â·18Â·17Â·16Â·15Â·14
B. 20Â·19Â·18Â·17Â·16Â·15Â·14/(7!13!)
C. 20!/(7!13!)
D. (20!/(3!17!))Â·(20!/(4!16!))
E. (20!/(3!17!))Â·(17!/(4!13!))

OA is E,

Why not D, Can someone explain this to me please. Thanks in advance.

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Director
Joined: 07 Nov 2004
Posts: 683

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10 Nov 2004, 20:57
Ashok, I believe the reason its E is that,

The 20 job applicants can fill the 3 secretarial positions 20C3 ways. Once the 3 positions are filled there are only 17 candidates left and they can fill the remaining 4 sales position 17C4 ways.

So total ways to fill the 7 positions = 20C3 * 17C4 = (20!/(3!17!))Â·(17!/(4!13!))

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Joined: 31 Dec 1969

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Location: Russian Federation
GMAT 3: 740 Q40 V50
GMAT 4: 700 Q48 V38
GMAT 5: 710 Q45 V41
GMAT 6: 680 Q47 V36
GMAT 9: 740 Q49 V42
GMAT 11: 500 Q47 V33
GMAT 14: 760 Q49 V44
WE: Supply Chain Management (Energy and Utilities)

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10 Nov 2004, 21:31
gayathri wrote:
Once the 3 positions are filled there are only 17 candidates left

This is what I was missing...

Great...thanks...!

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10 Nov 2004, 21:31
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