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In how many ways can seven vacancies at a company be filled

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Intern
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In how many ways can seven vacancies at a company be filled [#permalink] New post 09 Sep 2005, 11:01
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 eight of the applicants have applied for the secretarial positions, and the remaining 12 have applied for the sales rep positions.


a. 20!/(7!13!)
b. (20!/(3!17!))·(20!/(4!16!))
c. (20!/(3!17!))·(17!/(4!13!))
d. 20·19·18·20·19·18·17
e. (12!/(3!12!))·(8!/(4!8!))
f. (8!/(3!17!))·(12!/(4!13!))
g. (8!/(3!8!))·(12!/(4!12!))
h. Not enough information is given to answer this question.
Senior Manager
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 [#permalink] New post 09 Sep 2005, 12:13
C(8,3)*C(12,8)
=(8!/(3!(5!))*(12!(8!)(4!))
=65*495 = 32,175
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 [#permalink] New post 09 Sep 2005, 15:02
The OA is g.

I couldnt understand how they got to g but if anyone can, please explain.
Senior Manager
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 [#permalink] New post 09 Sep 2005, 17:36
coffeeloverfreak wrote:
C(8,3)*C(12,8)
=(8!/(3!(5!))*(12!(8!)(4!))
=65*495 = 32,175


Never mind, was reading too fast. That should be C(8,3)*C(12,4).
  [#permalink] 09 Sep 2005, 17:36
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