# 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.

• Maybe it means, not including P-A-N-T-A? Sep 2, 2015 at 5:38
• For arranged it should be $60$. For rearranged there would be a case for either $119$ or $59$. Sep 2, 2015 at 5:38
• I think you're right. For the wrong result 59, it probably because the question want you to find how many ways can they be rearranged but there is a typo. Sep 2, 2015 at 5:39
• @AndréNicolas: What do u mean by rearranged ?
– R K
Sep 2, 2015 at 5:39
• Changing the positions of the letters. But the word used in the problem is arranged, and then PATNA is a valid arrangement. Sep 2, 2015 at 5:42

The question should be framed as "In how many ways can it be rearranged". Then $$59$$ would be right. Otherwise, $$60$$ is the answer.