[" In how many different ways can the letters of the "],[" word 'MATHEMATICS' be arranged,so that the vowels "],[" always come together? "]

In how many ways can the letters of the word MATHEMATICS' be arranged so that vowels always come together?

In how many different ways can the letters of the word 'DIRECTOR' be arranged so that the vowels are always together?

In how many different ways can the letters of the word TRANSPIRATION' be arranged so that the vowels always come together? (a) 2429500 (b) 1360800 (c) 1627800 (d) None of these

In how many different ways can the letters of the word 'DESIGN' be arranged so that the vowels are at the two ends?

In how many different ways can the letters of the word 'DIGEST' be arranged so that the vowels are never together?

In how many different ways can the letters of the word CAPITAL be arranged in such a way that the vowels always come together? (a) 120 (b) 360 (c) 720 (d) 840(e) None of these

In how many different ways can the letters of the word CORPORATION be arranged in such a way that the vowels always come together? (a) 810 (b) 1440 (c) 2880 (d) 50400 (e) 5760