JEE Main & Advanced Mathematics Permutations and Combinations Question Bank Critical Thinking Questions

  • question_answer How many numbers between 5000 and 10,000 can be formed using the digits 1, 2, 3, 4, 5, 6, 7, 8, 9 each digit appearing not more than once in each number [Karnataka CET 1993]

    A) \[5{{\times }^{8}}{{P}_{3}}\]

    B) \[5{{\times }^{8}}{{C}_{3}}\]

    C) \[5\ !\ {{\times }^{8}}{{P}_{3}}\]

    D) \[5\ !\ {{\times }^{8}}{{C}_{3}}\]

    Correct Answer: A

    Solution :

    A number between 5000 and 10,000 can have any of the digits 5, 6, 7, 8, 9 at thousand's place. So thousand's place can be filled in 5 ways. Remaining 3 places can be filled by the remaining 8 digits in \[^{8}{{P}_{3}}\] ways. Hence required number =\[5{{\times }^{8}}{{P}_{3}}\].


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