Question

How many integer numbers between 0 and 9999 are there that have exactly one digit 1 and exactly one digit 3?

Answer 1

There are no 1 digit numbers that work.

There are only 2 2 digit numbers that work.

There are 7⋅2⋅1+2⋅2⋅8=46 numbers that are 3 digit

There are 7⋅3⋅2⋅8+2⋅3⋅8⋅8=720 4 digit numbers

So we have 768 numbers that work