JEE Main & Advanced Mathematics Probability Question Bank Use of permutations and combinations in probability

  • question_answer
    Word ?UNIVERSITY? is arranged randomly. Then the probability that both ?I? does not come together, is [UPSEAT 2001]

    A)            \[\frac{3}{5}\]                          

    B)            \[\frac{2}{5}\]

    C)            \[\frac{4}{5}\]                          

    D)            \[\frac{1}{5}\]

    Correct Answer: C

    Solution :

                       Total number of ways \[=\frac{10\,!}{2\,!}\]                    Favourable number of ways for \['I'\] come together is \[9\,!\]                    Thus probability that \['I'\] come together                    \[=\frac{9\,!\,\times \,2\,!}{10\,!}=\frac{2}{10}=\frac{1}{5}\].                    Hence required probability \[=1-\frac{1}{5}=\frac{4}{5}.\]


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