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 1

Number of ways in which three letters put into three envelopes = 3! = 6
Number of ways in which one letter put in correct envelope ${=}^3{C}_1\times 1=3$
Number of ways in which two letter put in correct envelope = 1
Number of ways in which atleast one letter put in correct envelope = 3 + 1 = 4
thus probability that atleast one letter put in correct envelope $=\frac{4}{6}=\frac{2}{3}.$