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

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Intern
Joined: 27 Aug 2005
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In how many ways can seven vacancies at a company be filled [#permalink]  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!))Â·(20!/(4!16!))
c. (20!/(3!17!))Â·(17!/(4!13!))
d. 20Â·19Â·18Â·20Â·19Â·18Â·17
e. (12!/(3!12!))Â·(8!/(4!8!))
f. (8!/(3!17!))Â·(12!/(4!13!))
g. (8!/(3!8!))Â·(12!/(4!12!))
h. Not enough information is given to answer this question.
Senior Manager
Joined: 27 Aug 2005
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C(8,3)*C(12,8)
=(8!/(3!(5!))*(12!(8!)(4!))
=65*495 = 32,175
Intern
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The OA is g.

I couldnt understand how they got to g but if anyone can, please explain.
Senior Manager
Joined: 27 Aug 2005
Posts: 332
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Kudos [?]: 42 [0], given: 0

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).
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