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 \[1\times 243+2\times 27+3\times 1=300\].
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