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Probability

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by Imsukhi » Sat Jun 22, 2013 4:09 am
There are 10 envelopes and 10 letters to go inside them. Each letter is menat for a specified envelope only. What is the probability that exactly 9 of them are in the right envelope?

a)1/10!
b)0
c)1
d)9/10
E) none of above
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by Brent@GMATPrepNow » Sat Jun 22, 2013 4:18 am
Imsukhi wrote:There are 10 envelopes and 10 letters to go inside them. Each letter is menat for a specified envelope only. What is the probability that exactly 9 of them are in the right envelope?

a)1/10!
b)0
c)1
d)9/10
E) none of above
The answer is [spoiler]0 (B)[/spoiler].
If 9 of the letters were in the correct envelope, it would be impossible for the 10th letter not to be in its correct envelope. At that point, there would be only one envelope remaining, and since the other envelopes were "properly" filled, the remaining envelope would have to match the remaining letter.

Cheers,
Brent

since it's impossible for
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by snigdha1605 » Sat Jun 22, 2013 9:08 am
Hi Brent,

Wouldn't this problem translate to the probability of getting all of the letters in their correct envelopes which would be 1/10! ?

Total no of ways of placing the letters in the envelopes = 10!
No of ways of placing correct letters within their corresponding envelopes = 1

Regards,
Snigdha
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by Imsukhi » Sat Jun 22, 2013 9:43 am
Hi Snigdha,

Brent is rite. The probability is zero.
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by Brent@GMATPrepNow » Sat Jun 22, 2013 10:33 am
snigdha1605 wrote:Hi Brent,

Wouldn't this problem translate to the probability of getting all of the letters in their correct envelopes which would be 1/10! ?

Total no of ways of placing the letters in the envelopes = 10!
No of ways of placing correct letters within their corresponding envelopes = 1

Regards,
Snigdha
The question asks for the probability that exactly exactly 9 letters are in the right envelope. This is different from asking for the probability that all 10 letters are in the right envelope.

Since it's impossible for exactly 9 letters to be in the right envelope, the probability is zero.

Cheers,
Brent
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by snigdha1605 » Sat Jun 22, 2013 11:26 am
Thanks Brent...Got it now
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