Question

The number of $5$ letters palindrome words that can be formed only using vowels is

• A. $24$
• B. $25$
• C. $125$
• D. $250$

Answer 1

The correct option is C $125$

Let the palindrome word is $A_1{A}_2{A}_3{A}_2{A}_1$, then
$A_1$ can be filled in $5$ ways $(a,e,i,o,u)$,
similarly $A_2$ can be filled in $5$ ways,
similarly $A_3$ can be filled in $5$ ways,
$\therefore$total number of palindrome words $=5\times 5\times 5=125$