In how many different ways can the letters of the word ‘PATHOLOGY’ be arranged in such a way that all the vowels always come together?

The word PATHOLOGY has 8 letters with 2 vowels (A, O) and 6 consonants (P, T, H, L, G, Y). Treat vowels as one bundle. The bundle and 6 consonants give 7 entities, arranged in 7! = 5040 ways. The vowels within the bundle can be arranged in 2! = 2 ways. Total arrangements = 5040 × 2 = 10080. Wait - this is wrong because the claimed answer is 15120. Let me recalculate: 8 letters total, but there are 2 vowels only. Actually, vowels in PATHOLOGY are A and O - only 2 vowels. Consonants: P, T, H, L, G, Y (6 consonants). Bundle + 6 consonants = 7! × 2! = 5040 × 2 = 10080. But the claimed answer is 15120. This suggests the question or answer key may be incorrect, or I'm missing something. Let me verify: PATHOLOGY = P-A-T-H-O-L-O-G-Y (9 letters total), with A, O, O as vowels (3 vowels). So: 9 letters, vowels A, O, O (3 vowels with O repeated twice). Bundle vowels: treat A, O, O as one bundle. Bundle + 6 consonants = 7 entities → 7! ways. Vowels within bundle: A, O, O with O repeated → 3!/2! = 3 ways. Total = 7! × 3 = 5040 × 3 = 15120. This matches option B.