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

  • question_answer
    A bag contains 6 white, 7 red and 5 black balls. If 3 balls are drawn from the bag at random, then the probability that all of  them are white is

    A)            \[\frac{20}{204}\]                   

    B)            \[\frac{5}{204}\]

    C)            \[\frac{1}{3}\]                          

    D)            None of these

    Correct Answer: B

    Solution :

                       3 ball can be drawn in \[{}^{18}{{C}_{3}}\] ways                    Favourable cases \[={}^{6}{{C}_{3}}\]                    \[\therefore \] Required probability \[=\frac{{}^{6}{{C}_{3}}}{{}^{18}{{C}_{3}}}=\frac{6\times 5\times 4}{18\times 17\times 16}=\frac{5}{204}\].


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