Counting principle

Hi,

How many integers are there between 100 and 1000 all of whose digits are odd?

I know the answer to this: 125.

How is the counting principle to be used in solving this?

There are 5 odd digits: 1, 3, 5, 7, 9
How many numbers with all odd digits are between 100 and 1000?
Isn't this just how many 3 digit numbers have all odd digits?

# 3 odd digit numbers = (# possible odd digits for 1st digit) x (# possible odd digits for 2nd digit) x (# possible odd digits for 3rd digit)
= 5 x 5 x 5 = ...