We have a question that asks to find the number of integers between 1 and 100 that are divisible by 2,3 or 5. So i use the sum rule let E,F and G be the the integers. so, n(EUFUG) = n(E) + n(F) + n(G) - n(EnF) - n(EnG) - n(FnG) but this doesn't work. it gives me the answer of 70 but the actual answer is 74. Since I know the answer is 74 this one doesn't matter but the next question asks to find the number of integers between 1 and 100000. So it's obvious that I cant count them. just to make sure I did the above part right n(EUFUG) would be 100/2 + 100/3 + 100/5 - 100/6 - 100/10 - 100/15 correct? I hope somone can figure out where i've gone wrong.