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

  • question_answer
    A committee consists of 9 experts taken from three institutions A, B and C, of which 2 are from A, 3 from B and 4 from C. If three experts resign, then the probability that they belong to different institutions is [Roorkee Qualifying 1998]

    A)            \[\frac{1}{729}\]                     

    B)            \[\frac{1}{24}\]

    C)            \[\frac{1}{21}\]                       

    D)            \[\frac{2}{7}\]

    Correct Answer: D

    Solution :

                       Required probability                                                               \[=\frac{{}^{2}{{C}_{1}}\times {}^{3}{{C}_{1}}\times {}^{4}{{C}_{1}}}{{}^{9}{{C}_{3}}}=\frac{2\times 3\times 4}{\left( \frac{9\times 8\times 7}{3\times 2} \right)}=\frac{2}{7}\].


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