How many distinct linear permutations can you make using the letters from FLOOWNEDEN?

Question

Shadow · Answer

Basically how many different layouts can you have, using the letters "FLOOWNEDEN"

cancer · Answer

I know what permutations are. I don't know how to solve it. It's not 10!.

cancer · Answer

It also has to be a distinct permutation, so I'm not sure if I should divide it by 2! ?

cancer · Answer

Due to the repeat letters

Ultrilliam · Answer

If I understood shadow correctly...
FLOOWNEDEN = 10 letters...
How many possibilities is there with those 10 letters?

Shadow · Answer

Mhm yeah, distinct

cancer · Answer

I understand that.. but I don't know what to do when it says it's distinct lol

Shadow · Answer

Yeah it means no repetitions, so O, N, and E cannot repeat

Shadow · Answer

$$\frac{ 10! }{ 2!^{3} }$$

Basically it's all the variations of 10!, but ensuring distinction by taking out the variations  by which the letters repeat. Since there are 2 letters, we get 2!. But there are three of these,( O, N, E) so we do 2! times 2! times 2! or 2!^3