How many ways can you rearrange the letters of the word OPTICAL so that the vowels are all next to each other?

Question

How many ways can you rearrange the letters of the word OPTICAL so that the vowels are all next to each other. For example OIAPTCL?

Answer 1

There are 3 vowels and 4 consonants. Here are the ways of arranging the letters so that all vowels, first regardless of order, are next to each other

VVVCCCC, CVVVCCC, CCVVVCC, CCCVVVC, CCCCVVV

I count 5 ways of arranging without order. Now, accounting for order, within each of the 5 ways shown above, there are 3*2*1 = 6 ways of arranging 3 vowels and 4*3*2*1 = 24 ways of arranging 4 consonants.

According to my calculator, 5*6*24 = 720 ways or rearranging the letters of "OPTICAL"