Number of 5 letter palindromes given 7 possible letters 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:

$125$
$225$
$343$
$729$

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.
**HINT:**Think about how many ways you have to choose the first letter, then the second, then the third and so on...
Pick the first center letter. At the right side you have a permutation of 7 letters in two i.e you 42 left and right letters for each center letter. So you will have 42x7 = 294 then add aa, bb, hh, ii,...for each center letter you will have 49 more. So the answer is c.