Last visit was: 23 Apr 2026, 08:42 It is currently 23 Apr 2026, 08:42
Home
Messages
Tests
Schools
Events
Close
GMAT Club Daily Prep
Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track
Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 962
Own Kudos:
798
Posts: 962
Kudos: 798
There are three secretaries who work for four departments. 24 Jan 2005, 22:35
Kudos
Add Kudos
Bookmarks
Bookmark this Post
00:00
Start Timer
Pause Timer
Resume Timer
Show Answer
Hide
Show
History
N
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!

Difficulty:

(N/A)

Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions

History

Date
Time
Result
Not Attempted Yet
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?



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
banerjeea_98
User avatar
Joined: 18 Nov 2004
Last visit: 17 May 2012
Posts: 674
Own Kudos:
201
Posts: 674
Kudos: 201
There are three secretaries who work for four departments. 25 Jan 2005, 10:17
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Total possibilities = 4x4x4 (all 3 can get all 4 reports)

Favorable outcome = 3 possibilities

p(e) = 3/64.....is that correct ?
User avatar
banerjeea_98
User avatar
Joined: 18 Nov 2004
Last visit: 17 May 2012
Posts: 674
Own Kudos:
201
Posts: 674
Kudos: 201
There are three secretaries who work for four departments. 25 Jan 2005, 10:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
HongHu
Why is the favorable outcome only 3?
Show more

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 ?
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 962
Own Kudos:
798
Posts: 962
Kudos: 798
There are three secretaries who work for four departments. 25 Jan 2005, 10:34
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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.
User avatar
Vijo
User avatar
Joined: 01 Jan 2005
Last visit: 11 Jul 2005
Posts: 76
Own Kudos:
8
Location: NJ
Posts: 76
Kudos: 8
There are three secretaries who work for four departments. 25 Jan 2005, 11:18
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Favorable outcomes = 3

total no of possibilities = 15

3/15=1/5.

Plz tell theOA.
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 962
Own Kudos:
798
Posts: 962
Kudos: 798
There are three secretaries who work for four departments. 25 Jan 2005, 22:28
Kudos
Add Kudos
Bookmarks
Bookmark this Post
OA is 3C1*4C2*2P2/3^4
Anybody can explain this?
User avatar
davinci
User avatar
Joined: 26 Jan 2005
Last visit: 29 Jan 2005
Posts: 4
Own Kudos:
2
Posts: 4
Kudos: 2
There are three secretaries who work for four departments. 26 Jan 2005, 08:36
Kudos
Add Kudos
Bookmarks
Bookmark this Post
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?
avatar
HongHu
avatar
Joined: 03 Jan 2005
Last visit: 25 Apr 2011
Posts: 962
Own Kudos:
798
Posts: 962
Kudos: 798
There are three secretaries who work for four departments. 26 Jan 2005, 09:16
Kudos
Add Kudos
Bookmarks
Bookmark this Post
Ahh, that makes great sense. Thanks a bunch!



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Problem Solving (PS) Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
Moderator:
Bunuel
Math Expert
109778 posts