Three letters are dictated to three persons and an envelope is address

1.	Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the enveloped at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.
Answer» Total number of ways of putting three letters into three envelopes is 3P₃ = 3! (ways) = 6. The number of ways in which none of the letter is put into proper envelope is 2. ∴ P(none) = 2/6 = 1/3 ∴ p(atleast one letter is in its proper envelop) = 1 - p (none) = 1 - 1/3 = 2/3

Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the enveloped at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

Answer»

Total number of ways of putting three letters into three envelopes is

3P₃ = 3! (ways) = 6.

The number of ways in which none of the letter is put into proper envelope is 2.

∴ P(none) = 2/6 = 1/3

∴ p(atleast one letter is in its proper envelop) = 1 - p (none)

= 1 - 1/3 = 2/3

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Three letters are dictated to three persons and an envelope is addressed to each of them, the letters are inserted into the enveloped at random so that each envelope contains exactly one letter. Find the probability that at least one letter is in its proper envelope.

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