Question:
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 envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Answer:
Given
Number of letters = 3
Number of envelope = 3
Total number of ways in which letters put in 3 envelope = 3! = 6
Number of ways in which one letter put in correct envelope = 3 ( Either in 1st envelope or in 2nd envelope or in 3rd envelope )
Number of ways in which two letters or all the 3 letters put in correct envelope = 1
So Total number of ways in which atleast one letter is put in correct envelope = 3+1 = 4
Now the probability that at least one letter is in its proper envelope = 4/6 = 2/3
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