Question

How many whole numbers between 100 and 800 contain the digit 2?

• A. 200
• B. 214
• C. 220
• D. 240
• E. 248

Hint:

For “contains a digit” problems, count the complement (numbers without that digit) and subtract from the total. Be careful with the allowed range of the leading digit; here hundreds digit is only \(1\)–\(7\).

Answer 1

The Correct Option is B

Step 1: The numbers between 100 and 800 are the 3-digit integers from \(100\) to \(799\). Hence the hundreds digit \(h\in\{1,2,3,4,5,6,7\}\) (7 choices); tens and ones digits can be \(0\)–\(9\) (10 choices each). Total numbers \(=7\times10\times10=700\).
Step 2: Use complement counting (exclude digit \(2\) in all places).
Hundreds digit cannot be \(2\): \(h\in\{1,3,4,5,6,7\}⇒ 6\) choices.
Tens digit \(\neq 2\): \(9\) choices.
Units digit \(\neq 2\): \(9\) choices.
Numbers with no digit \(2\): \(6\times9\times9=486\).
Step 3: Numbers containing at least one \(2\): \[ 700-486=214. \] Therefore, the required count is \(\boxed{214}\).