[Math] In how many ways can the letters of the word $PATNA$ be arranged

Question

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.

Answer 1

They mean other ways of arranging the letters. So the result is what you found minus the original word: 59.