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

 Messages: [ Previous | Next ]
 Ben Brink Posts: 201 From: Rosenberg, TX Registered: 11/11/06
RE: number of onto functions
Posted: May 19, 2012 4:59 PM
 att1.html (1.3 K)

Dr. Scales:
Have never seen this approach before. Thanks.
Ben

> Date: Sat, 19 May 2012 11:22:08 -0400
> From: discussions@mathforum.org
> To: discretemath@mathforum.org
> Subject: Re: number of onto functions
>

> > 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.
> >

> Mahesh,
>
> 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 4.3.2 ways.
>
> So answer = 1 . 6.5.4 . 4.3.2 = 2880 I think.
>
> Regards, Peter Scales.

Date Subject Author
5/19/12 Mahesh
5/19/12 Ben Brink
5/19/12 Peter Scales
5/19/12 Ben Brink
5/20/12 Peter Scales