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JEE Main & Advanced Mathematics Probability Question Bank Self Evaluation Test - Probability-II

  • question_answer
    Three letters are written to three different persons and addresses on the three envelopes are also written. Without looking in the addresses, the letters are kept in these envelopes. The probability that all the letters are not placed into their right envelopes is

    A) \[\frac{1}{2}\]

    B) \[\frac{1}{3}\]

    C) \[\frac{1}{6}\]

    D) \[\frac{5}{6}\]

    Correct Answer: B

    Solution :

    [b] Favourable ways \[=3!\left( 1-\frac{1}{1!}+\frac{1}{2!}-\frac{1}{3!} \right)=2\] Total ways = 3! \[\therefore \] Required probability \[=\frac{2}{3!}=\frac{1}{3}\]


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