In how many wys casn the letters of the word INTERMEDIATE be arranged among themselves so that no two vowels may occupy consecutive places?

In how many different ways can the letters of the word 'VIRTUAL ' be arranged among themselves ?

In how many ways can the letters of the word INTERMEDIATE be arranged so that: the vowels always occupy even places? the relative order of vowels and consonants do not alter?

In how many ways can the letters of the word STRANGE be arranged so that the vowels may appear in the odd places?

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

In how many ways can the letters of the word INSURANCE be arranged , so that vowels are occupied at even 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 'DIRECTOR' be arranged, so that the three vowels are never together?