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Tanya prepared 4 different letters to 4 different addresses

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Tanya prepared 4 different letters to 4 different addresses. For each letter, she prepared one envelope with its correct address. If the 4 letters are to be put into the four envelopes at random, what is the probability that only one letter will be put into the envelope with its correct address?

A. 1/24
B. 1/8
C. 1/4
D. 1/3
E. 3/8

Official Answer

1 Answer

Ankit Saxena
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Let's say you put the correct letter for the first envelope. Now the others have to be wrong combinations.
That gives the probability as
(Correct One of the 4) * (Incorrect 2 of the remaining 3) * (Incorrect one of the remaining 2) * 1
= 1/4 * 2/3 * 1/2 * 1 = 1/12
Now, you could have chosen any of the other 3 envelopes to put the correct letter in and similar scenarios would have been observed.
So answer should be 1/12 * 4 = 1/3 . D.
answered Jun 20, 2015 by Beginner (1 point)
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