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

  • question_answer
    If four persons are chosen at random from a group of  3 men, 2 women and 4 children. Then the probability that exactly two of them are children, is [Kurukshetra CEE 1996; DCE 1999]

    A)            \[\frac{10}{21}\]                     

    B)            \[\frac{8}{63}\]

    C)            \[\frac{5}{21}\]                       

    D)            \[\frac{9}{21}\]

    Correct Answer: A

    Solution :

                       Total number of ways \[={}^{9}{{C}_{4}},\] 2 children are chosen in \[{}^{4}{{C}_{2}}\] ways and other 2 persons are chosen in \[{}^{5}{{C}_{2}}\] ways.                    Hence required probability =\[\frac{{}^{4}{{C}_{2}}\times {}^{5}{{C}_{2}}}{{}^{9}{{C}_{4}}}=\frac{10}{21}.\]


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