In how many different ways can the letters of the word ‘DETAIL’ be arranged so that the vowels occupy only the odd positions?

In how many different ways can the letters of the word MACHINE be arranged so that the vowels may occupy only the odd positions? (a) 210 (b) 576 (c) 144 (d) 1728 (e) 3456

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

how many different ways can the letters of word 'DIVISION' can be arranged?

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 'DESIGN' be arranged so that the vowels are at the two ends?

In how many ways can the letters of the word VIOLENT be arranged so that vowels ocupy only the odd places?

In how many ways can the letters of the word VIOLENT be arranged so that vowels ocupy only the odd places?

In how many ways can the letters of the word FAILURE be arranged so that the consonants may occupy only odd positions?