## mathmath333 one year ago In how many ways can the letters of the word PATNA be arranged ?

1. mathmath333

\large \color{black}{\begin{align} & \normalsize \text{In how many ways can the letters of the word PATNA be arranged ?}\hspace{.33em}\\~\\ & a)\ 60 \hspace{.33em}\\~\\ & b)\ 120 \hspace{.33em}\\~\\ & c)\ 119 \hspace{.33em}\\~\\ & d)\ 59 \hspace{.33em}\\~\\ \end{align}}

2. steve816

Hey there! We can simply use factorials to figure this out! Let's do this!!! There are 5 letters, so the number of combination would be 5! but wait, there are 2 A's, and they can be interchanged and still would be the same, so we have to divide by 2!$\frac{ 5! }{ 2! }=60$

3. steve816

So the answer is A! There you have it, Algebra 2 honors class was complete hell, but it was worth it just to answer your question :)

4. mathmath333

but the answer given in book is d.)59

5. steve816