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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
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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