TITLE: How many three digit numbers are not divisible by 3, 5 or 11?
QUESTION [11 upvotes]: How many three digit numbers are not divisible by 3, 5, or 11?
How can I solve this?
Should I look to the divisibility rule or should I use, for instance, 
$$
  \frac{999-102}{3}+1
$$

REPLY [4 votes]: One can compute the required exclusions/inclusions quickly and avoid having to deal with floor function by going about it as below:
Numbers from 1 to 990 not divisible by $3, 5$ or $11$ = $990(1-\frac{1}{3})(1-\frac{1}{5})(1-\frac{1}{11})$ = 480
One can count that from 991 to 999 there are 5 such numbers.
Total numbers between 1 - 999 => $485$
Total numbers from 1 to 99 not divisible by $3,5$ or $11$ = $99(1-\frac{1}{3})(1-\frac{1}{5})(1-\frac{1}{11})$ = 48
Total 3 digit numbers not divisible by $3, 5$ or $11$ = $485 - 48$ = $437$