how many 3 digit numbers can be formed using 0-9 with at least 1 repeating digits?
1. First, we find the number of 3 digit numbers.
2. Second, we find the number of 3 digit numbers with NO repeating digits.
3. Third, we subtract the result of 2 from the result of 1
1. There are two ways to do step 1
A. there are 999 1 digit, 2-digit and 3-digit numbers.
there are 99 of these which are not 3 digits
we subtract 99 from 999 and get 900
B. There are 9 ways to pick the first digit, 10 ways to pick the
second digit, and 10 ways to pick the thrid digit, so that's
91010 = 900.
Either way you get 900 3-digit numbers
2. To do step 2, there are 9 ways to choose the first digit,
(can't choose 0), 9 ways to choose the 2nd digit (can choose 0),
and 8 ways to choose the third digit. That's 998 = 648
3. 900 - 648 = 252
Edwin
