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Seeking conceptual clarity on Permutation

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Seeking conceptual clarity on Permutation

by RBBmba@2014 » Tue Nov 25, 2014 10:23 pm
HI Math Experts,
This is not exactly any question from any Test prep companies. Rather it's just a basic question to get some clarification on my doubts, so that I can have better understanding of the actual problem.

Here's the question -
In how many ways can a person post 5 letters in 4 letter boxes ?

And here goes my doubts -
Method 1: Say, there are 4 boxes - A,B,C & D that need to be filled by the 5 letters L1 to L5.

Now, L1 can be posted in either A, B, C, or D i.e. 4 ways. This holds good for other letters(L2/3/4/5) as well.

So the total no of ways in which 5 letters can be posted in 4 boxes will be 4 x 4 x 4 x 4 x 4 = 4^5=1024.

Now, another option coming to my mind -
Method 2: A can be filled in by either L1, L2, L3,L4, or L5 i.e. 5 ways. B in 4 ways, C in 3 ways and D in 2 ways (i.e. total 5 x 4 x 3 x 2=120 ways). Still one letter remaining which can be posted in any of the 4 boxes i.e 4 ways.

So the total no of ways in which 5 letters can be posted in 4 boxes or 4 boxes can be filled in by 5 letters, will be 120 x 4 =480.

Now, any of these two should be the proper method. Can you please explain which one is so and WHY ?

Would much appreciate your detail explanation.

Thank you!
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by GMATinsight » Wed Nov 26, 2014 2:00 am
RBBmba@2014 wrote:HI Math Experts,
This is not exactly any question from any Test prep companies. Rather it's just a basic question to get some clarification on my doubts, so that I can have better understanding of the actual problem.

Here's the question -
In how many ways can a person post 5 letters in 4 letter boxes ?

And here goes my doubts -
Method 1: Say, there are 4 boxes - A,B,C & D that need to be filled by the 5 letters L1 to L5.

Now, L1 can be posted in either A, B, C, or D i.e. 4 ways. This holds good for other letters(L2/3/4/5) as well.

So the total no of ways in which 5 letters can be posted in 4 boxes will be 4 x 4 x 4 x 4 x 4 = 4^5=1024.

Now, another option coming to my mind -
Method 2: A can be filled in by either L1, L2, L3,L4, or L5 i.e. 5 ways. B in 4 ways, C in 3 ways and D in 2 ways (i.e. total 5 x 4 x 3 x 2=120 ways). Still one letter remaining which can be posted in any of the 4 boxes i.e 4 ways.

So the total no of ways in which 5 letters can be posted in 4 boxes or 4 boxes can be filled in by 5 letters, will be 120 x 4 =480.

Now, any of these two should be the proper method. Can you please explain which one is so and WHY ?

Would much appreciate your detail explanation.

Thank you!
First method is correct because as per the question there is no restriction on more than 1 letters to go in any letter box
So you must consider all cases
1) all letters in 1 box
2) All letters in two boxes (3, 2) or (2, 3)
3) All letters in three boxes
4) All letters in 4 boxes

However Second Method is WRONG because it only considers the scenario that all letters in 4 boxes with only one box having two letters.


Method 2 only considers (1, 1, 1, 2) which is not the only case as all cases are mentioned above therefore method 2 would be correct if each letter box were to have minimum 1 letter

I hope it answers your question
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by Mathsbuddy » Wed Nov 26, 2014 7:35 am
RBBmba@2014 wrote:HI Math Experts,
This is not exactly any question from any Test prep companies. Rather it's just a basic question to get some clarification on my doubts, so that I can have better understanding of the actual problem.

Here's the question -
In how many ways can a person post 5 letters in 4 letter boxes ?

And here goes my doubts -
Method 1: Say, there are 4 boxes - A,B,C & D that need to be filled by the 5 letters L1 to L5.

Now, L1 can be posted in either A, B, C, or D i.e. 4 ways. This holds good for other letters(L2/3/4/5) as well.

So the total no of ways in which 5 letters can be posted in 4 boxes will be 4 x 4 x 4 x 4 x 4 = 4^5=1024.

Now, another option coming to my mind -
Method 2: A can be filled in by either L1, L2, L3,L4, or L5 i.e. 5 ways. B in 4 ways, C in 3 ways and D in 2 ways (i.e. total 5 x 4 x 3 x 2=120 ways). Still one letter remaining which can be posted in any of the 4 boxes i.e 4 ways.

So the total no of ways in which 5 letters can be posted in 4 boxes or 4 boxes can be filled in by 5 letters, will be 120 x 4 =480.

Now, any of these two should be the proper method. Can you please explain which one is so and WHY ?

Would much appreciate your detail explanation.

Thank you!
Method two omits the scenario when box 1 has no letters, etc...
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by [email protected] » Wed Nov 26, 2014 11:48 pm
Hi RBBmba@2014,

I'm all for the acquisition of knowledge, but if you're focused on GMAT-centric studying then you'd probably be better served citing specific GMAT questions. The general example that you posted here is a really rare version of a permutation question (one that you probably would NOT see on the Official GMAT).

Since this is clearly about Quant, I'm curious about how you've performed on your practice CATs (and the Official GMAT, if you've already taken it). What are/were your Quant Scaled Scores? Do you tend to get more questions wrong because of a silly/little mistake or because the question was too hard?

GMAT assassins aren't born, they're made,
Rich
Contact Rich at [email protected]
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by GMATinsight » Thu Nov 27, 2014 4:13 am
I have a slightly different opinion about the possibility of such question to be asked in Official GMAT as some students have reported some such questions in past (Without reproducing the exact question).
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by RBBmba@2014 » Thu Nov 27, 2014 6:35 am
GMATinsight wrote:
RBBmba@2014 wrote:HI Math Experts,
This is not exactly any question from any Test prep companies. Rather it's just a basic question to get some clarification on my doubts, so that I can have better understanding of the actual problem.

Here's the question -
In how many ways can a person post 5 letters in 4 letter boxes ?

And here goes my doubts -
Method 1: Say, there are 4 boxes - A,B,C & D that need to be filled by the 5 letters L1 to L5.

Now, L1 can be posted in either A, B, C, or D i.e. 4 ways. This holds good for other letters(L2/3/4/5) as well.

So the total no of ways in which 5 letters can be posted in 4 boxes will be 4 x 4 x 4 x 4 x 4 = 4^5=1024.

Now, another option coming to my mind -
Method 2: A can be filled in by either L1, L2, L3,L4, or L5 i.e. 5 ways. B in 4 ways, C in 3 ways and D in 2 ways (i.e. total 5 x 4 x 3 x 2=120 ways). Still one letter remaining which can be posted in any of the 4 boxes i.e 4 ways.

So the total no of ways in which 5 letters can be posted in 4 boxes or 4 boxes can be filled in by 5 letters, will be 120 x 4 =480.

Now, any of these two should be the proper method. Can you please explain which one is so and WHY ?

Would much appreciate your detail explanation.

Thank you!
First method is correct because as per the question there is no restriction on more than 1 letters to go in any letter box
So you must consider all cases
1) all letters in 1 box
2) All letters in two boxes (3, 2) or (2, 3)
3) All letters in three boxes
4) All letters in 4 boxes

However Second Method is WRONG because it only considers the scenario that all letters in 4 boxes with only one box having two letters.


Method 2 only considers (1, 1, 1, 2) which is not the only case as all cases are mentioned above therefore method 2 would be correct if each letter box were to have minimum 1 letter

I hope it answers your question
GMATinsight - thanks for clarifying!
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by GMATinsight » Thu Nov 27, 2014 6:44 am
RBBmba@2014 wrote:
GMATinsight - thanks for clarifying!
You forgot to click on "Thank" Button :P ;)
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by RBBmba@2014 » Thu Nov 27, 2014 7:28 am
[email protected] wrote:Hi RBBmba@2014,

I'm all for the acquisition of knowledge, but if you're focused on GMAT-centric studying then you'd probably be better served citing specific GMAT questions. The general example that you posted here is a really rare version of a permutation question (one that you probably would NOT see on the Official GMAT).

Since this is clearly about Quant, I'm curious about how you've performed on your practice CATs (and the Official GMAT, if you've already taken it). What are/were your Quant Scaled Scores? Do you tend to get more questions wrong because of a silly/little mistake or because the question was too hard?

GMAT assassins aren't born, they're made,
Rich
Rich - As I said it's not from any test prep companies. It just came into my mind, perhaps while browsing forum posts or thinking (a bit deep) about these sort of problems! Somehow it arose and I got confused even after getting the correct method. Hence the post :-)

BTW,sent you a PM on your 2nd question!
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by RBBmba@2014 » Thu Nov 27, 2014 7:34 am
GMATinsight wrote:
RBBmba@2014 wrote:
GMATinsight - thanks for clarifying!
You forgot to click on "Thank" Button :P ;)
Ah! sorry. Done Sir :-)
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