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

The word EPENTHESIS has 10 letters with E appearing 3 times, T appearing 2 times, S appearing 2 times, and vowels E, E, I (3 vowels). Treat vowels as one unit: 8 total units (7 consonants + 1 vowel group) with E(3), T(2), S(2) repetitions. Internal arrangement of vowels = 3!/3! = 1. Total = 8!/(3! × 2! × 2!) × 1 = 40320/(6 × 2 × 2) = 40320/24 = 1680. This doesn't match options. Wait - rechecking: vowels are E, E, I = 3 letters, but E repeats. Vowels together as one unit means we have EPNTHSS + (EEI) = 8 units total. 8!/(2! × 2!) for consonants (E, T, S in consonants). Actually need to be more careful about which letters repeat where. Let me recount: EPENTHESIS - E(3), P(1), N(1), T(2), H(1), S(2), I(1). Vowels = E, E, I. Consonants = P, N, T, H, T, S, S (7 letters with T twice, S twice, E once removed). So consonants arrange as 7!/(2! × 2!) = 5040/4 = 1260. Vowels internally: 3!/3! = 1. Total = 1260 × 1 = 1260. Still doesn't match. Rereading the question - it asks specifically for arrangements where vowels come together. The calculation I did gives 1260, but option B is 10080. Let me verify: 10 letters total, E(3), T(2), S(2). If vowels must be together, treat them as one block. But actually 10080 = 10!/12 = 3628800/12... hmm. Actually 10080 × 12 = 120960, not matching. Let me reconsider: maybe the word has different letters? EPENTHESIS: E-P-E-N-T-H-E-S-I-S. Counting: E=3, P=1, N=1, T=2, H=1, S=2, I=1. Total 10. 10!/(3! × 2! × 2!) = 3628800/(6 × 2 × 2) = 3628800/24 = 151200 total arrangements. With vowels together: treat E,E,I as one unit. We have 8 units. But E appears both in vowels and... no wait. Let me recalculate. Total without restriction: 10!/(3! × 2! × 2!) = 151200. With vowels together: The 3 vowels (E, E, I) form one block. Within the block, they can be arranged in 3!/3! = 1 way (since E repeats). Total arrangements = 8! × 1 = 40320. But this doesn't account for the repeated E's outside the vowel block. Actually, I need to reconsider what the vowel block contains vs consonants. Consonants: P, N, T, H, T, S, S (7 letters, T twice, S twice). Vowels: E, E, I (3 letters, E thrice). The consonants arrange in 7!/(2! × 2!) = 1260 ways. Place the vowel block in one of 8 positions (before, between, or after consonants). Total = 1260 × 8 = 10080. Yes, that's option B.