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

  • question_answer
    A bag contains 3 red, 7 white and 4 black balls. If three balls are drawn from the bag, then the probability that all of them are of the same colour is

    A)            \[\frac{6}{71}\]                       

    B)            \[\frac{7}{81}\]

    C)            \[\frac{10}{91}\]                     

    D)            None of these

    Correct Answer: C

    Solution :

                       Required probability \[=\frac{{}^{3}{{C}_{3}}+{}^{7}{{C}_{3}}+{}^{4}{{C}_{3}}}{{}^{14}{{C}_{3}}}\]                                                                             \[=\frac{1+35+4}{14\,.\,13\,.\,2}=\frac{40}{14\,.\,26}=\frac{10}{91}.\]


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