Question

In how many different ways can the letters of word 'OPTICAL' be arranged so that the vowels always come together?

Answer 1

The vowels can be placed in the word, so they're next to each other, in
`5\cdot3!=5\cdot6=30` ways. The reaming 4 letters can be arranged in
`4!=24` ways.

So, the answer is
`30\cdot24=720` ways.