# 2 Problems on Palindrome of Five Letters: A Letter appears more than twice and no letter does so.

A sequence of letters of the form $abcba$, where the expression is unchanged upon reversing order, is an example of a palindrome (of five letters).

(a) if a letter may appear more than twice, how many palindromes of five letters are there? of six letters

(b) Repeat part (a) under the condition that no letter appears more than twice

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So, what are yourr thoughts on the questions? How far can you get? what do you know about permutations? Why are you interested in this particular problem? – Gerry Myerson Feb 9 '13 at 5:12
for part (a) : I use this way, There are four possibilities form of the palindrome, they are aaaaa ; baaab; ababa; aabaa; the possibilities of the first form is 26, the possibilities of the second form is 26 x 25 the possibilities of the third form is also 26 x 25 the possibilities of the fourth form is 26 x 25 so, the number of palindromes of five letters with a letter may appear more than twice is 26 + (3 x 36 x 25) is this correct? – chihiroasleaf Feb 9 '13 at 5:13
I think you've left out abcba. – Gerry Myerson Feb 9 '13 at 5:16
hhmm..., so I should add (26 x 25 x 24) ? and it will be 6 + (3 x 36 x 25) + (26 x 25 x 24) right? – chihiroasleaf Feb 9 '13 at 5:21
Looks good, except that 36 looks like a typo. – Gerry Myerson Feb 9 '13 at 5:23