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There are three secretaries who work for four departments. [#permalink]

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24 Jan 2005, 22:35

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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?

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 ?

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.

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.