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

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CEO
Joined: 15 Aug 2003
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In how many ways can seven vacancies at a company be filled [#permalink]  29 Sep 2003, 11:01
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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.
Intern
Joined: 17 Sep 2003
Posts: 31
Location: Mumbai,India
Followers: 0

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

3 secretarial posiitons can be filled in 20x19x18 ways
4 sales position can be filled in 20x19x18x17 ways

Total number of ways= 20x20x19x19x18x18x17

IS THIS CORRECT?
SVP
Joined: 03 Feb 2003
Posts: 1608
Followers: 6

Kudos [?]: 76 [0], given: 0

If we had had 7 people for the seven positions, the answer would have been 7!/(3!*4!). But since we have 20 applicants, we should choose 7 from 20 at first=20C7.

Therefore, [20C7*7!]/[3!*4!]=2713200
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