How many three digit numbers can be formed using the digits 1,2,3,4,5,6,7,8 and 9?

For this questions, there are two situations

$a)$ When repetition is not allowed

There are 9 numbers and we want to form 3 digit numbers. Three digit numbers that can be formed is, $^6P_3={9\times8\times7\times6!\over 6! }=9\times8\times7=504$ numbers.

Therefore when repetition is not allowed, we can form 504 three digit numbers.

$b)$ When repetition is allowed.

When we are allowed to repeat digits, then there are $9^3=729$ three digit numbers that can be formed.

Therefore, when repetition is allowed, we can form 729 three digit numbers.