find the number of palindromes with 6 digits that can be formed using the digits

(1) 0, 2, 4, 6, 8 (2) 1, 3, 5 , 7 , 9

(1) Since we need 6 digit palindromes, we cannot count those numbers that begin with 0.

Two example palindroms are 4 4 0 0 2 2, and 6 4 2 2 4 6.

As we can see, the 1st and 6th place can be filled with four digits - 2, 4, 6 and 8. And the rest can be filled with 5 digits - 0, 2, 4, 6, 8.

So required number of palindromes $=4\times 5\times 5=100$

(2) No restriction is placed here. So by similar logic, required number of palindromes $=5\times 5\times 5=125$