SOLUTION: this question is from the text book of class xi of chapter permutation and combination and the question is ..... three letters are dictated to three persons and an envelope is add

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Question 183108: this question is from the text book of class xi of chapter permutation and combination and the question is .....
three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each enveloped contains exactly one letter. find the probability that one letter is in its proper enveloped.
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the envelopes at random so that each enveloped contains exactly one letter. find the probability that one letter is in its proper enveloped.

Suppose letters A, B, and C should go in envelopes
A, B, and C, respectively.

There are only three ways this can successfully occur

1. Letter A was correctly placed in envelope A
   Letter B was incorrectly placed in envelope C
   Letter C was incorrectly placed in envelope B

2. Letter A was incorrectly placed in envelope C 
   Letter B was correctly placed in envelope B
   Letter C was incorrectly placed in envelope A
 
3. Letter A was incorrectly placed in envelope B
   Letter B was incorrectly placed in envelope A
   Letter C was correctly placed in envelope C 

There are 3! or 3x2x1 or 6 ways they can be placed
anywhere, so the desired probability is

3%2F6 or 1%2F2

Edwin