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

  • question_answer
    Ten students are seated at random in a row. The probability that two particular students are not seated side by side is

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

    B)            \[\frac{3}{5}\]

    C)            \[\frac{2}{5}\]                          

    D)            \[\frac{1}{5}\]

    Correct Answer: A

    Solution :

                       Total ways \[=10\,\,!\]                    Two boys can sit side by side in \[2\times 9\,\,!\] ways.                    So probaibility \[=\frac{2\times 9\,\,!}{10\,\,!}=\frac{1}{5}\]            Thus the probability that they are not seated together is \[1-\frac{1}{5}=\frac{4}{5}.\]


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