Discover All Permutations of "Dinner" or "Diner

[#neutrino]

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?

 

[tommyxu3]

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 $\frac{6!}{2!}=360.$