Question

A palindrome is a word, number, phrase or sequence of words that reads the same backwards as forwards e.g. "SOLOS".
The number of palindromes that can be formed using the letters ''AABBBBCCCDDDD'' is

• A. $\frac{6!}{2!}$
• B. $\frac{6!}{2!\times 2!}$
• C. $\frac{7!}{2!\times 2!}$
• D. $\frac{8!}{4!\times 4!}$

Answer 1

The correct option is B $\frac{6!}{2!\times 2!}$

AABBBBCCCDDDD
Here we have $2A,4B,3C,4D$
So, total $13$ letters.
Letter $C$ must be in middle of word.
Word must be in the form of
$------C------$
So, we put $1A,2B,1C,2D$ on the left side of $C$ which can be done in $\frac{6!}{2!\times 2!}$ ways.