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There are three secretaries who work for four departments.

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There are three secretaries who work for four departments.  [#permalink] New post 24 Jan 2005, 21:35
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There are three secretaries who work for four departments. If each of the four departments have one report to be typed out, and the reports are randomly assigned to a secretary, what is the probability that all three secretary are assigned at least one report?
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 [#permalink] New post 25 Jan 2005, 09:17
Total possibilities = 4x4x4 (all 3 can get all 4 reports)

Favorable outcome = 3 possibilities

p(e) = 3/64.....is that correct ?
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 [#permalink] New post 25 Jan 2005, 09:28
HongHu wrote:
Why is the favorable outcome only 3?

One secretary has to get 2 reports as there r 4 reports and 3 secretary and each one has to get atleast 1.....so 3 ways u can give 2 reports to 1 secretary. Is the OA different ?
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 [#permalink] New post 25 Jan 2005, 09:34
I don't have the OA right now. I think you are right but I have to go home to check. (Don't remember it as I never understood how to do it.)

When you do total possibilities, the 4 for each person means 1 report, 2 reports, 3 reports, 4 reports? But won't the next person's possibility affected by how many the first one got? I'm totally confused here.
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 [#permalink] New post 25 Jan 2005, 10:18
Favorable outcomes = 3

total no of possibilities = 15

3/15=1/5.

Plz tell theOA.
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 [#permalink] New post 25 Jan 2005, 21:28
OA is 3C1*4C2*2P2/3^4
Anybody can explain this?
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 [#permalink] New post 26 Jan 2005, 07:36
There are 4 reports
There are 3 secretaries.

Now for first report, u have got 3 options.
For second report, u have got 3 options.
Similarly.. for third and fourth reports.

Therefore, total options = 3*3*3*3 = 81

Now, for each secretary to get atleast one we can have an arrangement like this:
211
121
112

So basically it boils down to giving an extra report to one secretary. We select 1 secretary as 3C1. We select 2 reports for this secretary as 4C2. After giving out these reports, we are left with 2 reports and 2 secretaries. This can be done in 2 ways.

Therefore, we have 3C1*4C2*2 = 3*6*2=36

Therefore answer is 36/81 = 4/9
Is that fine?
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 [#permalink] New post 26 Jan 2005, 08:16
Ahh, that makes great sense. Thanks a bunch!
  [#permalink] 26 Jan 2005, 08:16
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