Number of 5 letter palindromes given 7 possible letters

Question

A 5 letter word is formed using some of the letters {a,b,h,i,p,r,s}.

How many of them will be palindromes?

Options:

1. $125$
2. $225$
3. $343$
4. $729$

My Approach:

Only the middle number can be arranged in $7$ ways. Rest all the numbers can be arranged like Whatever the first letter from right should be last letter from left. Whatever the second letter from start should be last letter from left.

But i am not able to get to the solution.

Can anyone give me the hint to solve the problem.

Answer 1

**HINT:**Think about how many ways you have to choose the first letter, then the second, then the third and so on...

Answer 2

Pick one of the $7$ letters as the middle letter, another one as the second and fourth letter, and finally one more for the first and last letter.

Assuming repetitions are allowed, there are $7\cdot7\cdot7$ ways to do this.