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

  • question_answer
    Twenty tickets are marked the numbers 1, 2, ..... 20. If three tickets be drawn at random, then what is the probability that those marked  7 and 11 are among them

    A)            \[\frac{3}{190}\]                     

    B)            \[\frac{1}{19}\]

    C)            \[\frac{1}{190}\]                     

    D)            None of these

    Correct Answer: A

    Solution :

                       \[7,\,\,11\] have always to be in that group of three, therefore 3rd ticket may be chosen in 18 ways.                    Hence required probability is \[\frac{18}{{}^{20}{{C}_{3}}}=\frac{18\,.\,3\,.\,2}{20\,.\,19\,.\,18}=\frac{3}{190}\].


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