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

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In how many ways can seven vacancies at a company be filled [#permalink]  29 Sep 2003, 11:04
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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 eight of the applicants have applied for the secretarial positions, and the remaining 12 have applied for the sales rep positions.
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Re: PS : Counting Methods # 12 [#permalink]  29 Sep 2003, 18:26
praetorian123 wrote:
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.

Sec
8C3 = 8*7*6/3*2*1 = 56

Sales
12C4 = 12*11*10*9/4*3*2*1 = 495

56*495 = 27720

Could be way off here?
Re: PS : Counting Methods # 12   [#permalink] 29 Sep 2003, 18:26
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