mathmath333
  • mathmath333
In how many ways can the letters of the word PATNA be arranged ?
Mathematics
schrodinger
  • schrodinger
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{In how many ways can the letters of the word PATNA be arranged ?}\hspace{.33em}\\~\\ & a)\ 60 \hspace{.33em}\\~\\ & b)\ 120 \hspace{.33em}\\~\\ & c)\ 119 \hspace{.33em}\\~\\ & d)\ 59 \hspace{.33em}\\~\\ \end{align}}\)
steve816
  • 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!\[\frac{ 5! }{ 2! }=60\]
steve816
  • 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 :)

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mathmath333
  • mathmath333
but the answer given in book is d.)59
steve816
  • steve816
Then your book is drunk.
midhun.madhu1987
  • midhun.madhu1987
A repeats 2 times in PATNA... will that have any impact?? Not sure...

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