In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?
Choose the most appropriate option:
A) 120990
B) 120950
C) 120970
D) 120960
E) 120980
8!(2!)(2!)=8×7×6×5×4×3×2×1/(2×1)(2×1)   =10080   In the 4 vowels (AEAI), 'A' occurs 2 times and rest of the vowels are different.   Number of ways to arrange these vowels among themselves =4!/2!=4×3×2×12×1=12   Hence, required number of ways   =10080×12=120960   Answer: 120960
<result>D</result>
In how many different ways can the letters of the word 'MATHEMATICS' be arranged such that the vowels must always come together?