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# In a department store there are 30 cubbies of different

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Intern
Joined: 29 Apr 2006
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In a department store there are 30 cubbies of different [#permalink]  22 May 2006, 06:13
In a department store there are 30 cubbies of different hats.
Each hat has its own assigned cubbie box. However, there was
an earthquake...and all of the hats fell onto the floor (out
of their cubbies) and then the department store lady tried to
put back the hats into their cubbies...so randomly she placed
one hat here...and one hat there until 30 hats were in the
cubbies (one per cubbie). However, of course, the store lady did
not know which hat went with which cubbie, so some of the cubbies
had the wrong hat in them... the question is: what is the probability
that at least one hat will be in its properly assigned cubbie?
Intern
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here is my explanation .
answer = 1-(probability that all the hats are placed wrong )

probability that all the hats are placed wrong = fact(29)/ fact(30) = 1/30
Director
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guptaraja said

here is my explanation .
answer = 1-(probability that all the hats are placed wrong ) ---- this is right...

probability that all the hats are placed wrong = fact(29)/ fact(30) = 1/30
--------- this is wrong.
Senior Manager
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mahesh004 wrote:
guptaraja said

here is my explanation .
answer = 1-(probability that all the hats are placed wrong ) ---- this is right...

probability that all the hats are placed wrong = fact(29)/ fact(30) = 1/30
--------- this is wrong.

1- (29/30)^30

There is only one problem - after puting the first hat in wrong cubbie the probability of 2nd hat to be placed incorrectly could be 28/29 or 29/29 ....

This may not be as easy as it looks unless we take a simplistic view.

Last edited by old_dream_1976 on 27 May 2006, 06:20, edited 1 time in total.
Manager
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old_dream_1976 wrote:
mahesh004 wrote:
guptaraja said

here is my explanation .
answer = 1-(probability that all the hats are placed wrong ) ---- this is right...

probability that all the hats are placed wrong = fact(29)/ fact(30) = 1/30
--------- this is wrong.

1- (29/30)^30

I am also getting 1-(29/30)^30. Whats the OA?
Intern
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shobhitb wrote:
old_dream_1976 wrote:
mahesh004 wrote:
guptaraja said

here is my explanation .
answer = 1-(probability that all the hats are placed wrong ) ---- this is right...

probability that all the hats are placed wrong = fact(29)/ fact(30) = 1/30
--------- this is wrong.

1- (29/30)^30

I am also getting 1-(29/30)^30. Whats the OA?

IMHO , this would have been right , if we were able to place more than 1 hat in a single box.

on thinking further , my answer is wrong too. agree with old_dream_1976, it is much more complicated than it seems.
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