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

  • question_answer
    Two numbers are selected randomly from the set \[S=\{1,\,2,\,3,\,4,\,5,\,6\}\] without replacement one by one. The probability that minimum of the two numbers is less than 4 is [IIT Screening 2003]

    A)            \[\frac{1}{15}\]                       

    B)            \[\frac{14}{15}\]

    C)            \[\frac{1}{5}\]                          

    D)            \[\frac{4}{5}\]

    Correct Answer: D

    Solution :

                       Total ways = 2! \[^{6}{{C}_{2}}=30\]                    Favourable cases \[=30-6=24\]                    \ Required probability \[=\frac{24}{30}=\frac{4}{5}\].


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