How many arrangements are possible from the letters (without repetition) of the word COMPUTER, such that vowels are never separated?

There are three vowels, viz. E, O & U which are not to be separated. Let us assume them to be one letter EOU, then we have got 5 (consonants) + 1(vowels group) = 6 letters which can be arranged in 6 X 5 X 4 X 3 X 2 X 1 = 720 ways. But EOU themselves can be arranged in 3 X 2 X 1 = 6 ways, so total possible arrangements are 720 X 6 = 4320 ways.