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Omni-MATH / Call a string of letters S an almost palindrome if S and the reverse of S differ in exactly two places. Find the number of ways to order the letters in HMMTTHEMETEAM to get an almo…

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problem

Call a string of letters SS an almost palindrome if SS and the reverse of SS differ in exactly two places. Find the number of ways to order the letters in HMMTTHEMETEAMH M M T T H E M E T E A M to get an almost palindrome.
Plain-text mathematical notation (without MathML)
Call a string of letters S an almost palindrome if S and the reverse of S differ in exactly two places. Find the number of ways to order the letters in HMMTTHEMETEAM to get an almost palindrome.
Original LaTeX notation
Call a string of letters $S$ an almost palindrome if $S$ and the reverse of $S$ differ in exactly two places. Find the number of ways to order the letters in $H M M T T H E M E T E A M$ to get an almost palindrome.

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