In how many different ways can the letters of the word Football be arranged such that all vowels are always together?

FOOTBALL has 8 letters. The vowels are O, O, A (3 letters). The consonants are F, T, B, L, L (5 letters).

Treat the three vowels as one block. Now arrange 6 items: the block and 5 consonants. L appears twice, so divide by 2!: 6!/2! = 720/2 = 360.

Inside the block, O, O, A can be arranged in 3!/2! = 3 ways.

Total = 360 × 3 = 1080 ways.