Number of 2-digit integers with at least one 4 = (total number of 2-digit integers) - (number of 2-digit integers that have ZERO 4's)

total number of 2-digit integers
We want to count the number of integers from 10 to 99 inclusive
A nice rule says: the number of integers from x to y inclusive equals y - x + 1
So the number of integers from 10 to 99 inclusive = 99 - 10 + 1 = 90

number of 2-digit integers that have ZERO 4's
Let's build some 2-digit integers that have ZERO 4's
The tens digit can be 1, 2, 3, 5, 6, 7, 8, or 9 (8 options)
The units digit can be 0, 1, 2, 3, 5, 6, 7, 8, or 9 (9 options)
So, the total number of 2-digit integers that have ZERO 4's = (8)(9) = 72

We get:
Number of 2-digit integers with at least one 4 = 90 - 72 = 18

Answer: C

Cheers,
Brent
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FACT: 1 to 99 there are 19 numbers which include digit 4 and 20 times digit 4 is used

But we need to exclude one 4 that comes between 1 and 10

so total numbers with digit 4 used = 19-1 = 18

Answer: Option C
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Solution

To find
We need to determine

• For how many of the integers from 10 to 99 is at least one of the two digits a 4

Approach and Working out

• Number of integers in which units digit is 4 = 9 {units digit can take any value from 1 to 9}
• Number of integers in which tens digit is 4 = 10 {units digit can take any value from 1 to 9}
• Number of integers in which both the digits are 4 = 1 {44}
• Thus, total number of such integers = 9 + 10 – 1 = 18

Thus, option C is the correct answer.

Correct Answer: Option C
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