JEE Main & Advanced Mathematics Probability Question Bank Definition of probability

  • question_answer
    There are 10 pairs of shoes in a cupboard from which 4 shoes are picked at random. The probability that there is at least one pair, is

    A)                 \[\frac{99}{323}\]

    B)                 \[\frac{224}{323}\]

    C)                 \[\frac{100}{323}\]             

    D)                 None of these

    Correct Answer: A

    Solution :

               Total number of ways \[=20\times 19\times 18\times 17\]                    The number of ways in which no pair is selected                    \[=20\times 18\times 16\times 14\]                    Hence the required probability                                                               \[=1-\frac{20\times 18\times 16\times 14}{20\times 19\times 18\times 17}=\frac{99}{323}.\]


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