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

  • question_answer
    An ordinary cube has four blank faces, one face marked 2 another marked 3. Then the probability of obtaining a total of exactly 12 in 5 throws, is

    A)            \[\frac{5}{1296}\]                   

    B)            \[\frac{5}{1944}\]

    C)            \[\frac{5}{2592}\]                   

    D)            None of these

    Correct Answer: C

    Solution :

                       \[n=\]Total number of ways \[={{6}^{5}}\]            \[A\] total of 12 in 5 throw can be obtained in following two ways ?                    (i) One blank and four \[3's={}^{5}{{C}_{1}}=5\]                    or (ii) Three \[2's\] and two \[3's={}^{5}{{C}_{2}}=10\]                    Hence, the required probability \[=\frac{15}{{{6}^{5}}}=\frac{5}{2592}.\]


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