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

  • question_answer
    Five digit numbers are formed using the digits 1, 2, 3, 4, 5, 6 and 8.  What is the probability that they have even digits at both the ends                                                                      [RPET 1999]

    A)            \[\frac{2}{7}\]                          

    B)            \[\frac{3}{7}\]

    C)            \[\frac{4}{7}\]                          

    D)            None of these

    Correct Answer: A

    Solution :

                       By using digits 1, 2, 3, 4, 5, 6 and 8, total 5 digits numbers = \[^{7}{{P}_{5}}\]                    And number of ways to form the numbers, they have even digit at both ends \[=4\times 3{{\times }^{5}}{{P}_{3}}\]                    \[\therefore \] Probability \[=\frac{4\times 3{{\times }^{5}}{{P}_{3}}}{^{7}{{P}_{5}}}=\frac{2}{7}\].


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