In how many ways can the letters of the word $PATNA$ be arranged? In how many ways can the letters of the word $PATNA$ be arranged ?


$a)\ 60 \\
 b)\  120 \\
 c)\ 119 \\
 \color{green}{d)\ 59 }\\
$

I thought it would be $\dfrac{5!}{2}=60$ but in book answer is given $59$ which puzzled me

I look for a short and simple way.

I have studied maths upto $12$th grade.
They mean other ways of arranging the letters. So the result is what you found minus the original word: 59.
The question should be framed as
"In how many ways can it be rearranged". Then $59$ would be right.
Otherwise, $60$ is the answer.