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

  • question_answer The number of times the digit 5 will be written when listing the integers from 1 to 1000 is

    A) 271

    B) 272

    C) 300

    D) None of these

    Correct Answer: C

    Solution :

    Since 5 does not occur in 1000, we have to count the number of times 5 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form\[xyz,\ 0\le x,\ y,\ z\le 9\]. The numbers in which 5 occurs exactly once\[={{(}^{3}}{{C}_{1}})\ .\ 9\times 9=243\]. The numbers in which 5 occurs exactly twice =\[{{(}^{3}}{{C}_{2}}.9)=27\] The numbers in which 5 occurs in all three digits \[=1\] Hence, the number of times 5 occurs is \[1\times 243+2\times 27+3\times 1=300\].


You need to login to perform this action.
You will be redirected in 3 sec spinner