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

  • question_answer
    In a box there are 2 red, 3 black and 4 white balls. Out of these three balls are drawn together. The probability of these being of same colour is                                                                   [MP PET 1996]

    A)            \[\frac{1}{84}\]                       

    B)            \[\frac{1}{21}\]

    C)            \[\frac{5}{84}\]                       

    D)            None of these

    Correct Answer: C

    Solution :

                       Total number of ways in which 3 balls can be drawn are \[{}^{9}{{C}_{3}}=84.\]            Since the drawn balls can?t be of red colour, as these are 2 in numbers.                    Therefore favourable number of ways \[={}^{3}{{C}_{3}}+{}^{4}{{C}_{3}}.\]                    Hence the required probability \[=\frac{5}{84}.\]


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