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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
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1- In how many ways can seven vacancies at a company be [#permalink]  10 Nov 2004, 19:47
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.
Director
Joined: 07 Nov 2004
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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!))
Joined: 31 Dec 1969
Location: India
Concentration: General Management, Strategy
GMAT 1: 710 Q49 V0
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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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