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probability - 4 letters to 4 envelopes

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probability - 4 letters to 4 envelopes  [#permalink]

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New post 04 Dec 2009, 11:56
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Tonya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelop with its correct address. If the 4 letters are to be put into the 4 envelops at random, what is the probability that only 1 letter will be put into the envelop with its correct address?

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Re: probability - 4 letters to 4 envelopes  [#permalink]

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New post 04 Dec 2009, 12:25
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kairoshan wrote:
Tonya prepared 4 different letters to be sent to 4 different addresses. For each letter, she prepared an envelop with its correct address. If the 4 letters are to be put into the 4 envelops at random, what is the probability that only 1 letter will be put into the envelop with its correct address?


Total # of ways of choosing envelopes=4!=24.
Only one letter in the right envelope: 4(# of envelopes)*2(# of ways possible to arrange 3 letters incorrectly in the envelopes, when one is correct)
ABCD(envelopes)
ACDB(letters)
ADBC(letters)
(When A is in the right envelope other three have only 2 possible incorrect arrangements)
As we have 4 letters, total # of ways 4*2=8

P(C=1)=8/24=1/3

To check all other possible scenarios check: letter-arrangements-understanding-probability-and-combinats-84912.html
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Re: probability - 4 letters to 4 envelopes  [#permalink]

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New post 30 Nov 2018, 23:13
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Re: probability - 4 letters to 4 envelopes &nbs [#permalink] 30 Nov 2018, 23:13
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