How many four-digit positive integers are there that have the digit 1?
attempt: There are $9000$ numbers that contains $4$ digits. Consider the case where we have $abcd$ where $abcd$ represent the digits. Then we would have $9$ choices for $a$ and $10$ choices for $b,c$ and assume last digit has $d = 1$ , so we would have $9(10)(10)(1)$ choices . Similarly if we assume at least $c = 1$, then we have $9$ choices for $a$ and $10$ choices for $b,d$ , so we have $9(10)(1)(10)$ choices, similarly when we consider the case if $a = 1$ and $b = 1$. Then we would to get the total four-digit positive integers such that contain the digit 1 to be $3700$. Can someone please verify this makes sense? Thank you!