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

  • question_answer
    A word consists of 11 letters in which there are 7 consonants and 4 vowels. If 2 letters are chosen at random, then the probability that all of them are consonants, is

    A)            \[\frac{5}{11}\]                       

    B)            \[\frac{21}{55}\]

    C)            \[\frac{4}{11}\]                       

    D)            None of these

    Correct Answer: B

    Solution :

               Required probability \[=\frac{{}^{7}{{C}_{2}}}{{}^{11}{{C}_{2}}}=\frac{7\,\,.\,\,6}{11\,\,.\,\,10}=\frac{21}{55}.\]


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