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.