How many different numbers can be formed when using 3 out of any 9
digits if they can be used more than once?
In most permutations, we are looking for a subset of the larger
set, and each member of the subset is only used once. In this
case, a digit can be used more than once, so the number of ways
each digit of the 3-digit number is selected is the same.
The number of ways the first digit is selected can be represented
by the permutation .
The formula for permutation is .
Substituting 9 for and 1 for , the result is
The second and third digit can also be determined this way, so the
number of different 3-digit numbers that can be formed is