In how many different ways can the letters of the word "MATRIX" be arranged such that the vowels always come together?
Explanation:
The word "MATRIX" has 6 letters: M, T, R, X (consonants) and A, I (vowels).
Treat the vowels (A, I) as a single unit or "pack". Now, we have 4 consonants + 1 pack = 5 entities to arrange.
The number of ways to arrange these 5 entities is 5! = 120.
Inside the pack, the vowels (A, I) can be arranged among themselves in 2! = 2 ways.
Total arrangements = 120 * 2 = 240.
