Discover All Permutations of "Dinner" or "Diner

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SUMMARY

The discussion focuses on calculating the permutations of the word "dinner," which contains repeated letters. The total permutations without considering indistinguishable letters is calculated as 6! (720). However, since the letter 'n' appears twice, the correct number of distinguishable permutations is determined using the formula 6! / 2! (360). This adjustment accounts for the repeated letters, leading to the conclusion that there are 360 unique permutations of the word "dinner."

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Homework Statement



How many different permutations can be created with the word dinner ?

Homework Equations

The Attempt at a Solution


Well if we consider all the permutations it will be
6P6 = 6*5*4*3*2*1 = 720 combinations --6!--
If we consider the distinguishable ones
Since 2N 's are present we can write as "diner" as it won't make a difference to the permutation and write as 5*4*3*2*1 =120 combinations does this make sense?
 
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My opinion:
The permutation of two 'n' doesn't make different, so the numbers of the permutation ##2!=2## can be regarded as one type. So, the answer should be ##\frac{6!}{2!}=360.##
 

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