Problem: In how many ways can these letters EFGHIEFGHI be arranged if the same letter musn't appear next to each other?

since we have 2 E's, F's, G's, H's and I's... The formula should be

10!

------------- = 113400 ways

2!2!2!2!2!

Then I combine similar letters [EE]FGHIFGHI for 5 letters

9!x5

-------- = 113400 ways

2!2!2!2!

That's where i get stumped... need help... XD