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InterviewSolution
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The number of times the digit 3 will be written when listing theintegers from 1 to 1000 is:300 (b) 269(c) 271 (d) 302A. 300B. 297C. 243D. 273 |
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Answer» Since 3 does not occur in 1000. So, we have to count the number of times 3 occurs when we list the integers from 1 to 999. Any number between 1 and 999 is of the form abc where `0lea,b,cle9`. Clearly, Number of times 3 occurs =(No. of number in which 3 occurs exactly at one place) +2 (No. of numbers in which 3 occurs exactly at two places) +3(No. of numbers in which 3 occurs exactly at three places) Now No. of numbers in which 3 occurs exactly at one place: Since 3 can occur at one place in `^(3)C_(1)` ways and each of the remaining two places can be filled in 9 ways. So, number of numbers in which 3 occurs exactly at one place `=^(3)C_(1)xx9xx9`. No. of number in which 3 occurs exactly at two places : Since 3 can occru exactly at two places in `^(3)C_(2)` ways and the remaining place can be filled in 9 ways. So, number of numbers in which 3 occurs exactly at two places `=""^(3)C_(2)xx9`. No. of numbers in which 3 occurs at all the three places: Since 3 can occur in all the three digits in one way only. So, number of numbers in which 3 occurs at all the three places is one. Hence, Numbers of times 3 occurs `=""^(3)C_(1)xx9xx9+2(""^(3)C_(2)xx9)+3xx1=300`. |
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