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# In how many ways can a person post 5 letters in 4 letter box

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In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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03 Feb 2013, 06:11
1
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Difficulty:

15% (low)

Question Stats:

71% (01:02) correct 29% (01:13) wrong based on 126 sessions

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In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 2^3
(B) 4^2
(C) 4^3
(D) 4^5
(E) 5^5

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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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03 Feb 2013, 07:55
1
Something is up with this question. Options (B) and (D) are exactly the same.

In my opinion, the correct solution for this is:

Arrange the 5 items in 4 different "baskets":
xxxxx|||

Total of 8!/(5!*3!) = 8.7 = 56

Now we can order these 5 items among themselves: 5! = 120 ways

Answer = 56*120 = 6720 IMO
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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03 Feb 2013, 10:47
3
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

There are 4 places (ABCD) that need to be filled.
Letter 1 can be posted in either A, B, C, or D i.e. 4 ways
Letter 2 can be posted in either A, B, C, or D i.e. 4 ways
Letter 3 can be posted in either A, B, C, or D i.e. 4 ways
Letter 4 can be posted in either A, B, C, or D i.e. 4 ways
Letter 5 can be posted in either A, B, C, or D i.e. 4 ways

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

Hope it helps.
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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Updated on: 04 Feb 2013, 09:45
Thanks Fameatop (1+)
After reading the problem again and realizing what the question was asking, your logic makes perfect sense.

Is caioguima's approach incorrect because we are counting certain letter box combos multiple times when we multiply by 5!?
Would caioguima's method be correct if the order of the letters in the boxes mattered?

Thanks to vips and debayan as well

Originally posted by holidayhero on 03 Feb 2013, 11:08.
Last edited by holidayhero on 04 Feb 2013, 09:45, edited 3 times in total.
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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03 Feb 2013, 11:17
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

Fameatop got it right.

For each letter the person has 4 options.
Thus 4*4*4*4*4=4^5=1024

Ans b and d are both correct. (Dude don't mind but watch for the source)
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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03 Feb 2013, 23:58
fameatop wrote:
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

There are 4 places (ABCD) that need to be filled.
Letter 1 can be posted in either A, B, C, or D i.e. 4 ways
Letter 2 can be posted in either A, B, C, or D i.e. 4 ways
Letter 3 can be posted in either A, B, C, or D i.e. 4 ways
Letter 4 can be posted in either A, B, C, or D i.e. 4 ways
Letter 5 can be posted in either A, B, C, or D i.e. 4 ways

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

Hope it helps.

fameatop-You're correct...!Honestly I was having confusion with this...but it appears really easy
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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04 Feb 2013, 00:04
Vips0000 wrote:
debayan222 wrote:
1.In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

Fameatop got it right.

For each letter the person has 4 options.
Thus 4*4*4*4*4=4^5=1024

Ans b and d are both correct. (Dude don't mind but watch for the source)

Vips0000-You got it too...!
And the source-it's one of the questions in IIM CAT materials of a CAT prep companies...unfortunately it's due to lack of proof-reading you know !

Not much we can do dude but just to point it out...
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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21 Apr 2018, 07:11
Top Contributor
bagdbmba wrote:
In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Take the task of distributing the 5 letters and break it into stages.

Stage 1: Select a box for the 1st letter to go into.
There are 4 available boxes, so we can complete stage 1 in 4 ways

Stage 2: Select a box for the 2nd letter to go into.
There are 4 available boxes, so we can complete stage 2 in 4 ways

Stage 3: Select a box for the 3rd letter to go into.
There are 4 available boxes, so we can complete stage 3 in 4 ways

Stage 4: Select a box for the 4th letter to go into.
There are 4 available boxes, so we can complete stage 4 in 4 ways

Stage 5: Select a box for the 5th letter to go into.
There are 4 available boxes, so we can complete stage 5 in 4 ways

By the Fundamental Counting Principle (FCP), we can complete all 5 stages (and thus distribute all 5 letters) in (4)(4)(4)(4)(4) ways (= 4⁵ ways)

Note: the FCP can be used to solve the MAJORITY of counting questions on the GMAT. So, be sure to learn it.

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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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08 May 2018, 11:12
I need help in my thought process:
why dont be solve it by slot method

- - - - for four letter box. and then , 1st place has 5 letters tro choose from then 2nd letter box had 4 letters to choose from?
5*4*3*2 ?
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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17 Dec 2018, 23:16
Each letter has 4 options.
So, total no of ways = 4 x 4 x 4 x 4 x 4 = 4^5
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Re: In how many ways can a person post 5 letters in 4 letter box  [#permalink]

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17 Dec 2018, 23:22
bagdbmba wrote:
In how many ways can a person post 5 letters in 4 letter boxes ?

(A) 480
(B) 1024
(C) 54
(D) 4^5
(E) 5^5

Bunuel- can you please explain in detail ?

Check out different cases of unfair distribution in these two posts on the Veritas blog:
https://www.veritasprep.com/blog/2011/1 ... inatorics-–-part-1/
https://www.veritasprep.com/blog/2011/1 ... s-part-ii/
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Re: In how many ways can a person post 5 letters in 4 letter box   [#permalink] 17 Dec 2018, 23:22
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