Question

The total number of permutations of the word ${}^{\prime }HARSHIT{A}^{\prime }$ such tha the word ${}^{\prime }AA{I}^{\prime }$ is always included

• A. $720$
• B. $1080$
• C. $2160$
• D. $360$

Answer 1

The correct option is D $360$

Consider the word
$HARSHITA$
Now considering 'AAI' together as one, then
$HHRST\left(AAI\right)$ we can arrange it in $\frac{6!}{2!}$ ...(due to repetition of H).
Now we cannot consider internal permutation of ${}^{\prime }AA{I}^{\prime }$ since we only want the word AAI
Hence the total number of words will be
$=\frac{6!}{2!}$
$=\frac{720}{2}$
$=360$.