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.

For arranged it should be $60$. For rearranged there would be a case for either $119$ or $59$. — André Nicolas, Sep 02 '15 at 05:38
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. — Asydot, Sep 02 '15 at 05:39
Rearrange means arrange them again but not be duplicated with original case. — Asydot, Sep 02 '15 at 05:42
Changing the positions of the letters. But the word used in the problem is arranged, and then PATNA is a valid arrangement. — André Nicolas, Sep 02 '15 at 05:42
There are 60 combinations, but only 59 of those are rearrangements as 1 of the 60 is the original. — mathreadler, Sep 02 '15 at 07:28
Does this answer your question? How to find the number of $k$-permutations of $n$ objects with $x$ types, and $r_1, r_2, r_3, \cdots , r_x$ = the number of each type of object? — , Feb 17 '23 at 11:54

score 2 · Accepted Answer · answered Sep 02 '15 at 05:45

2

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

answered Sep 02 '15 at 05:45

Julian Wittische

score -1 · Answer 2 · edited Jul 26 '19 at 19:23

-1

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

edited Jul 26 '19 at 19:23

Sambo

answered Jul 26 '19 at 17:52

Arman Khan

2 Answers2