# How many ways can the word “ARRANGER” be arranged?

I have tried this problem by doing 8 factorial over two times two factorial, which I got 10080, which doesn't seem to be right since the answer on the answer key is pretty far from my answer, can someone help me? Thank you
(I know this might be a duplicate of this question over here, but I can't understand the solution, any help will be appreciated)

• It might be helpful to say how you got 10080 so that someone can tell you where you went wrong. For reference's sake, the answer should be $8! / (2! 3!)$. – parsiad Feb 27 at 6:10
• can you explain a little or post it as a question? Thank you very much for your help though – Brian Zheng Feb 27 at 6:11
• You are pretty close. I think you're missing that ARRANGER has $3$ R's (while you accounted for $2$ R's by dividing by $2!$) and that the rest of your solution is fine. – Jason Kim Feb 27 at 6:16

## 1 Answer

The number of possible outcomes is a permutation in this case. The number of letters is 8 thus 8!, but you have two As and three Rs (which would lead to duplicates because switching R for R is afterall the same word) so divide by 2! and 3!. This leaves you with 3360 total unique outcomes.

• Thank you now I understand !!!! – Brian Zheng Feb 27 at 6:18