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

  • question_answer
    The probability that the three cards drawn from a pack of 52 cards are all red is                                          [MP PET 1999]

    A)            \[\frac{1}{17}\]                       

    B)            \[\frac{3}{19}\]

    C)            \[\frac{2}{19}\]                       

    D)            \[\frac{2}{17}\]

    Correct Answer: D

    Solution :

                       3 cards are drawn out of 26 red cards (favourable)                    \[=\frac{{}^{26}{{C}_{3}}}{{}^{52}{{C}_{3}}}=\frac{26\,\,!}{3\,\,!\,\,23\,\,!}\times \frac{3\,\,!\,\,49\,\,!}{52\,\,!}=\frac{2}{17}.\]


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