Answer to Question #89588 in Combinatorics | Number Theory for Aravind

Question

How many integers are there in between 1 and 500 divisible by 3 or 5

Answer 1

500/3= 166 numbers divisible by 3, 

500/5= 100 numbers divisible by 5. 

For a total of 

266 numbers are divisible by 3, 5 and their multiples. 

Now subtract the number of numbers divisible by 3x5 or 15, because these will have been counted twice, so 

500/15 = 33,

the result is 266-33 =233.

Answer: there are 233 numbers between 1 and 500 divisible by 3, 5.