NL-NWO 2006 Problem 1

A palindrome is a word that doesn't matter if you read it from left to right or from right to left. Examples: OMO, lepel and parterretrap. How many palindromes can you make with the five letters $a, b, c, d$ and $e$ under the conditions:

• each letter may appear no more than twice in each palindrome,
• the length of each palindrome is at least $3$ letters. (Any possible combination of letters is considered a word.)