how many arrangements are there of the letters COMMITTEE where none of the vowels are next to eachother? Thank you!
ignore the vowels, the consonents can go in 5!/(2!2!) = 2*3*5 = 30 ways to place the consonants
# C # M # M # T # T # 6 hashes that is where the vowels can go 6P4/(2!) = 180 ways
30*180 = 5400 ways (I think)