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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.

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  • $\begingroup$ Maybe it means, not including P-A-N-T-A? $\endgroup$ Sep 2, 2015 at 5:38
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    $\begingroup$ For arranged it should be $60$. For rearranged there would be a case for either $119$ or $59$. $\endgroup$ Sep 2, 2015 at 5:38
  • $\begingroup$ 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. $\endgroup$
    – Asydot
    Sep 2, 2015 at 5:39
  • $\begingroup$ @AndréNicolas: What do u mean by rearranged ? $\endgroup$
    – R K
    Sep 2, 2015 at 5:39
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    $\begingroup$ Changing the positions of the letters. But the word used in the problem is arranged, and then PATNA is a valid arrangement. $\endgroup$ Sep 2, 2015 at 5:42

2 Answers 2

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

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

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