Palindrome problem

Question

Let $F (n, k)$ be the number of length $n$ strings that can be formed using $k$ discrete digits. Let $G (n, k)$ be the number of length $n$ palindromic strings that can be formed using $k$ discrete digits. Find $G (21, 7)-G (20, 7)$

Options: $f (10, 7)$, $f (20, 7)$, $f (10, 6)$, $f(21,7)$ Please note that options have some constant multiplied with them (which I don't remember now. So any answer which has these options multiplied with some constant would be correct

So, I tried to solve this in the following way. For G(21,7). We have to find palindromic strings from 7 distinct digits. Since length of palindrome is 21. There will be 11 unique digits (not necessarily distinct). So for each digit we have 7 choices. So 7^11 are the total number of such palindromes. Similarly for G(20,7) 7^10 will be the possible palindromes. However on subtracting the two I am not able to get the answer. Am I wrong somewhere?

Answer 1

G(21,7)

That means 21-digit palindromic number. In order to form this number you use:

{a 10-digit number,let's say A}{any number from 0 to k-1}{the number A inverted, =one possible option}

so the possible combinations are F(10,7)*7*1

G(20,7)

That means 20-digit palindromic number. In order to form this number you use:

{a 10-digit number,let's say A}{the number A inverted, =one possible option}

so the possible combinations are F(10,7)*1

So:

$G(21,7)-G(20,7)=7*f(10,7)-F(10,7)=6*F(10,7)$