Find the number of positive integers less than 200 that are divisible by 3 or by 5, but not by 15.

Multiples of 3 below 200: ⌊199/3⌋ = 66. Multiples of 5: ⌊199/5⌋ = 39. Multiples of 15 (common to both): ⌊199/15⌋ = 13. By inclusion-exclusion, numbers divisible by 3 or 5 = 66+39−13 = 92. Since numbers divisible by 15 are counted once in this union but must now be excluded entirely, the required count = 92 − 13 = 79.