How many natural numbers are there between 100 and 1000 such that at least one of their digits is 6 ?

Step-by-step solution

The total number of natural numbers between 100 and 1000 is the set of all 3-digit numbers, which ranges from 100 to 999. The total count is 999 - 100 + 1 = 900 . To find the number of integers that have at least one digit as 6, it is easier to calculate the complement: the number of 3-digit integers that contain no digit equal to 6. For a 3-digit number d₁ d₂ d₃ where d₁ 1, 2, 3, 4, 5, 7, 8, 9 , d₂ 0, 1, 2, 3, 4, 5, 7, 8, 9 , and d₃ 0, 1, 2, 3, 4, 5, 7, 8, 9 , the number of choices for each digit is: For d₁ : 8 ch