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

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Director
Joined: 05 Jan 2005
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In how many ways can seven vacancies at a company be filled [#permalink]  20 Feb 2005, 05:55
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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.

Intern
Joined: 19 Feb 2005
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8C3 * 12C4 ??

or am i missing something here..
SVP
Joined: 30 Oct 2003
Posts: 1797
Location: NewJersey USA
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It is a metter of choosing 3 secretaries out of 8 and 4 sales res out of 12

8C3 * 12C4
VP
Joined: 18 Nov 2004
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8C3 * 12C4.....if the positions were not identical then we can't use this logic, then there will be more ways to choose.
Manager
Joined: 13 Feb 2005
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Location: Lahore, Pakistan
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yeah

3 sec and 4 sales out of 8 and 1 apps resp

8C3*12C4
Manager
Joined: 15 Feb 2005
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Location: Rockville
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12c4*8c3 here too
but what if the question asked either 4 positions of sales and 3 of secret. OR 3 positions of sales and 4 of secret.
would that be
12c4*8c3+12c3*8c4?
VP
Joined: 13 Jun 2004
Posts: 1123
Location: London, UK
Schools: Tuck'08
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I found the same result : 8C3 * 12C4

Senior Manager
Joined: 02 Feb 2004
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banerjeea_98 wrote:
8C3 * 12C4.....if the positions were not identical then we can't use this logic, then there will be more ways to choose.

can anybody pls explain the difference between identical and non-identical?
VP
Joined: 25 Nov 2004
Posts: 1495
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mirhaque wrote:
banerjeea_98 wrote:
8C3 * 12C4.....if the positions were not identical then we can't use this logic, then there will be more ways to choose.

can anybody pls explain the difference between identical and non-identical?

idetical=combination
non-idetical=permutation
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