There are 3 basic categories here, as there has to be at least one of one number, and two of the other two numbers. So we have:
So I take each these and permutate. Which gives me $3 \times 5!$ which is wrong. The answer is $90$. I know it is wrong because $3 \times 5! > 3^5$ which shouldn't be possible. I can't find any intuitive reason why my answer is wrong.
How did I approach it wrong?