How many 4 digit numbers between 3,000 and 7,999 contain at least one 2? How do I set this up?
You know that the 2's must appear in the last three digits. First figure out how many numbers between 000 and 999 have at least one 2 (hint: it's 1000 minus the quantity of numbers in that range that have no 2's). This is the same as the quantity of numbers that at least one 2 between 3000 and 3999, or 4000 and 4999, or 5000 and 5999, etc.
I suggest working this way: "How many numbers from $000$ to $999$ contain at least one two?"
The easy way to answer that is to find how many numbers from $000$ to $999$ do not contain at least one two.
We can use any digit other that a $2$- nine digits. Subtract that number from $999$.
Why do we need to multiply that number by five?