In base 5, how many two digit numbers are there?
To find the number of 2-digit numbers in base 10, we find:
1. for the first digit, there are 9 choices, as 0 is not admissible.
2. for the second digit, there are all of the 10 choices.
By the multiplication rule, the number of 2-digit base 10 numbers is (10-1)(10)=90.
You can do a similar counting for base 5 numbers.