### Instruction: How many four-digit positive integers are there with thousands digit $2?$.### Response: I want to count how many four-digit numbers have a $2$ in the thousands place, like $2,374$ or $2,000$.
To do this, I can fix the thousands digit as $2$ and then see how many choices I have for the other three digits.
For the hundreds digit, I can pick any of the ten digits from $0$ to $9$, so that gives me $10$ choices.
For the tens digit, I also have $10$ choices, regardless of what I picked for the hundreds digit.
For the units digit, I again have $10$ choices, no matter what I picked for the tens digit.
So, for each choice of the hundreds digit, I have $10 \times 10 = 100$ ways to complete the number, and since I have $10$ choices for the hundreds digit, I have $10 \times 100 = 1,000$ ways to make a four-digit number with $2$ in the thousands place.