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10 Nov 2004, 20:47
Kudos
Bookmarks
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. 20·19·18·17·16·15·14
B. 20·19·18·17·16·15·14/(7!13!)
C. 20!/(7!13!)
D. (20!/(3!17!))·(20!/(4!16!))
E. (20!/(3!17!))·(17!/(4!13!))
OA is E,
Why not D, Can someone explain this to me please. Thanks in advance.
A. 20·19·18·17·16·15·14
B. 20·19·18·17·16·15·14/(7!13!)
C. 20!/(7!13!)
D. (20!/(3!17!))·(20!/(4!16!))
E. (20!/(3!17!))·(17!/(4!13!))
OA is E,
Why not D, Can someone explain this to me please. Thanks in advance.
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10 Nov 2004, 20:57
Kudos
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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!))·(17!/(4!13!))
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!))·(17!/(4!13!))
gayathri
This is what I was missing...
Great...thanks...!
Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
