Counting

The number of ways you can make an outfit with 3 shirts, 4 pants, and 6 shoes is 3*4*6. Similarly, the number of 4 digit numbers that do not contain a 3 would be 8*9*9*9. This is because there are usually 9 possible numbers for the first digit and 10 possible numbers for every other digit, but because 3 is excluded, there are 8 numbers for the first digit and 9 for all the others. For palindromes, the first digit has to match the last, second matches second to last, etc. So, for a 4 digit palindrome that does not contain 3, it would be 8*9*1*1, because the last two digits are already chosen by the first two.