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

  • question_answer
    Six cards are drawn simultaneously from a pack of playing cards. What is the probability that 3 will be red and 3 black

    A)            \[^{26}{{C}_{6}}\]              

    B)            \[\frac{^{26}{{C}_{3}}}{^{52}{{C}_{6}}}\]

    C)            \[\frac{^{26}{{C}_{3}}{{\times }^{26}}{{C}_{3}}}{^{52}{{C}_{6}}}\]              

    D)            \[\frac{1}{2}\]

    Correct Answer: C

    Solution :

               Required probability \[=\frac{{}^{26}{{C}_{3}}\,.\,{}^{26}{{C}_{3}}}{{}^{52}{{C}_{6}}}\].


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