3 secretaries 3 departments

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3 secretaries 3 departments

by faraz_jeddah » Thu Sep 12, 2013 12:02 am
There are 3 secretaries who work for three departments. if each of the three departments have one report to be typed out and the reports are randomly assigned to a secretary. what is the probability that all three secretaries are assigned atleast one report?

I dont have the answer options.

But here is my approach. I used the listing technique.

Each secretary can handle a max of all 3 reports and minimum of 0 reports. So the combinations are

0 0 3
0 3 0
3 0 0
2 1 0
2 0 1
1 1 1
1 2 0
1 0 2
0 2 1
0 1 2

That answer should be 1/10 but it seems the answer is [spoiler]2/9[/spoiler]. What am I missing?
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by ganeshrkamath » Thu Sep 12, 2013 12:14 am
faraz_jeddah wrote:There are 3 secretaries who work for three departments. if each of the three departments have one report to be typed out and the reports are randomly assigned to a secretary. what is the probability that all three secretaries are assigned atleast one report?

I dont have the answer options.

But here is my approach. I used the listing technique.

Each secretary can handle a max of all 3 reports and minimum of 0 reports. So the combinations are

0 0 3
0 3 0
3 0 0
2 1 0
2 0 1
1 1 1
1 2 0
1 0 2
0 2 1
0 1 2

That answer should be 1/10 but it seems the answer is [spoiler]2/9[/spoiler]. What am I missing?

Given :

1 report from each of the 3 departments to be handed out randomly to 3 secretaries.

Favorable cases:
Distribute the 3 reports = 3! = 6


Sample space:

Each report can go to any of the 3 secretaries.
Total possibilities = 3*3*3 = 27

Probability = 6/27 = [spoiler]2/9[/spoiler]

You have assumed that all the reports are identical, which is not true.

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by Java_85 » Thu Sep 12, 2013 11:00 am
At first, I did assume that all the reports are identical too, but you're right.
Thanks for the question faraz_jeddah.

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by GMATGuruNY » Thu Sep 12, 2013 11:32 am
faraz_jeddah wrote:There are 3 secretaries who work for three departments. if each of the three departments have one report to be typed out and the reports are randomly assigned to a secretary. what is the probability that all three secretaries are assigned atleast one report?
The first report irrelevant: it can be assigned to any of the 3 secretaries.
P(the second report is assigned to a different secretary from the first secretary) = 2/3.
P(the third report is assigned to a different secretary from the first two secretaries) = 1/3.
Since we want both of these events to happen, we multiply:
2/3 * 1/3 = 2/9.

For a trickier version of this problem, check here:

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