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

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BSchool Forum Moderator
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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
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75% (00:17) correct 25% (00:27) wrong based on 41 sessions

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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 ?
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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
2
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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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03 Feb 2013, 07:55
1
KUDOS
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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03 Feb 2013, 11:08
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

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] 04 Feb 2013, 00:04
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