Question

How many four-digit positive integers have exactly three same digits and at least one zero?

Answer 1

Let's calculate first, how many such numbers there are, where the same three digits are different form 0.

$\underbrace{1\cdot1\cdot1\cdot1}_{\text{XXX0}}\cdot\underbrace{9}_{\text{X=\{1,2,\ldots,9\}}}\cdot\underbrace{3}_{\text{XXX0,XX0X,X0XX}}=27$

Now, the numbers where there are three 0's. There are only 9 of those

$1000,2000,\ldots,9000$

So, there are $27+9=36$ such numbers.