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 proper envelope.

Question

Filo · Accepted Answer

Let L1​,L2​,L3​ be three letters 
and E1​,E2​,E3​ be their corresponding envelops 
respectively.There are 6 ways of inserting 3 letters in 3 envelops. These are as follows:L1​E1​,L2​E3​,L3​E2​L2​E2​,L1​E3​,L3​E1​L3​E3​,L1​E2​,L2​E1​L1​E1​,L2​E2​,L3​E3​L1​E2​,L2​E3​,L3​E1​L1​E3​,L2​E1​,L3​E2​There are 4 ways in which at least one letter is inserted in a proper envelope.Thus the required probability is =64​=32​

Question Text	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 proper envelope.
Answer Type	Text solution:1
Upvotes	150

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 proper envelope.

Text solutionVerified

Practice questions from similar books