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# GMATPrep Probability Question

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Senior Manager
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GMATPrep Probability Question [#permalink]  04 Aug 2006, 09:19

Tanya prepared 4 different letters to be prepared for 4 different addresses. For each letter, she prepared an envolope with the correct address. If the 4 letters are to be put in the 4 envolopes at random, what is the probability that only 1 letter will be put into the envolope with the correct address.

A (1/24)

B (1/8)

C (1/4)

D (1/3)

E (3/8)
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Senior Manager
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Re: GMATPrep Probability Question [#permalink]  04 Aug 2006, 09:36
agsfaltex wrote:

Tanya prepared 4 different letters to be prepared for 4 different addresses. For each letter, she prepared an envolope with the correct address. If the 4 letters are to be put in the 4 envolopes at random, what is the probability that only 1 letter will be put into the envolope with the correct address.

A (1/24)

B (1/8)

C (1/4)

D (1/3)

E (3/8)

Total ways = 4! = 24
Only one letter with correct addr. and three letters with wrong addr.
=> Assume you already put the letter with the correct addr.. then it becomes 3 letters with wrong addr..
Total ways of putting 3 letters with wrong addr. = 2*1*1 =2
Thus, 2*4 = 8 (since there are 4 letters)

8/24 = 1/3
D it is.
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Director
Joined: 17 Jul 2006
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King,
well answered. Now I'm really learning the probability.

Total possible outcomes = 24

After taking one envelope which is right for that address.

For each person, the probability of his/her wrong address would be 2 envelopes of remaining 3

so 2* 2*2 / 24 = 1/3

Reply me if I'm wrong in making assumptions.

Last edited by baski6 on 04 Aug 2006, 09:46, edited 1 time in total.
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Schools: Completed at SAID BUSINESS SCHOOL, OXFORD - Class of 2008
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D

Total ways = 4! = 24

Now lets see cases when letter 1 is in the right envelope
E1 E2 E3 E4
---------------
1.L1 L4 L2 L3
2.L1 L3 L4 L2
Only two cases. Similarly for other letters there are two cases each
Total ways for this = 4 * 2 = 8

Prob = 8/24 = 1/3
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SAID BUSINESS SCHOOL, OXFORD - MBA CLASS OF 2008

Senior Manager
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Thanks everybody..... [#permalink]  04 Aug 2006, 12:28
Its starting to make sense.
Thanks everybody.....   [#permalink] 04 Aug 2006, 12:28
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