Question

How many integers between 10000 and 99999, inclusive, are divisible by 3 or 5 or 7?

Answer 1

Answer: Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.

Step-by-step explanation:

Since we have given that

Integers between 10000 and 99999 = 99999-10000+1=90000

n( divisible by 3) = $\dfrac{90000}{3}=30000$

n( divisible by 5) = $\dfrac{90000}{5}=18000$

n( divisible by 7) = $\dfrac{90000}{7}=12857.14$

n( divisible by 3 and 5) = n(3∩5)=$\dfrac{90000}{15}=6000$

n( divisible by 5 and 7) = n(5∩7) = $\dfrac{90000}{35}=2571.42$

n( divisible by 3 and 7) = n(3∩7) = $\dfrac{90000}{21}=4285.71$

n( divisible by 3,5 and 7) = n(3∩5∩7) = $\dfrac{90000}{105}=857.14$

As we know the formula,

n(3∪5∪7)=n(3)+n(5)+n(7)-n(3∩5)-n(5∩7)-n(3∩7)+n(3∩5∩7)

$=30000+18000+12857.14-6000-2571.42-4258.71+857.14\\\\=48884.15$

Hence, there are approximately 48884 integers are divisible by 3 or 5 or 7.