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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
Posts: 33

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

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09 Sep 2005, 12:01
This topic is locked. If you want to discuss this question please re-post it in the respective forum.

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.

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Senior Manager
Joined: 27 Aug 2005
Posts: 331

Kudos [?]: 199 [0], given: 0

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09 Sep 2005, 13:13
C(8,3)*C(12,8)
=(8!/(3!(5!))*(12!(8!)(4!))
=65*495 = 32,175

Kudos [?]: 199 [0], given: 0

Intern
Joined: 27 Aug 2005
Posts: 33

Kudos [?]: 2 [0], given: 0

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09 Sep 2005, 16:02
The OA is g.

I couldnt understand how they got to g but if anyone can, please explain.

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Senior Manager
Joined: 27 Aug 2005
Posts: 331

Kudos [?]: 199 [0], given: 0

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09 Sep 2005, 18:36
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).

Kudos [?]: 199 [0], given: 0

09 Sep 2005, 18:36
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