Final answer:
To determine how many integers from 1 to 200 are multiples of 2, 3, or 5, we can use the concept of inclusion-exclusion principle. The count is 140.
Step-by-step explanation:
To determine how many integers from 1 to 200 are multiples of 2, 3, or 5, we can use the concept of inclusion-exclusion principle. We need to count the numbers that are divisible by each individual number (2, 3, and 5) and subtract the numbers that are divisible by the combination of these numbers (2*3=6, 2*5=10, and 3*5=15). This is because if we simply add the counts of the numbers divisible by each individual number, we would be counting the numbers divisible by the combination multiple times.
Counting the numbers divisible by 2: 200/2 = 100
Counting the numbers divisible by 3: 200/3 = 66
Counting the numbers divisible by 5: 200/5 = 40
Counting the numbers divisible by the combination of 2 and 3: 200/6 = 33
Counting the numbers divisible by the combination of 2 and 5: 200/10 = 20
Counting the numbers divisible by the combination of 3 and 5: 200/15 = 13
Adding the counts and subtracting the counts of the combinations: 100 + 66 + 40 - 33 - 20 - 13 = 140
Therefore, there are 140 integers from 1 to 200 that are multiples of 2 or 3 or 5.