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Topic: number of onto functions
Replies: 4   Last Post: May 20, 2012 7:11 AM

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Peter Scales

Posts: 192
From: Australia
Registered: 4/3/05
Re: number of onto functions
Posted: May 19, 2012 11:22 AM
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> Q: In how many ways can 7 different jobs be assigned
> to 4 different employees so that each employee gets
> atleast one job and the best employee gets the
> toughest job.


I tackled it this way:

Let the 7 jobs be T(oughest) + 6 and
let the 4 employees be B(est) + 3

Then B and T always go together, plus 6 other jobs between 4 employees who always get at least 1 job each.

Allocate 6 jobs one each to the other 3 employees in 6.5.4 ways, with 3 jobs over.

Allocate these 3 jobs to 4 employees in 4.4.4 ways,
because they need not go to different employees.

So answer = 1 . 6.5.4 . 4.4.4 = 7680 I think.

Regards, Peter Scales.

Message was edited by: Peter Scales on 19 May.

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