(i) There is no restriction on letters

The word VOWELS contain 6 letters.

The permutation of letters of the word will be 6! = 720 words.

(ii) Each word begins with

Here the position of letter E is fixed.

Hence, the rest 5 letters can be arranged in 5! = 120 ways.

(iii) Each word begins with O and ends with L

The position of O and L are fixed.

Hence the rest 4 letters can be arranged in 4! = 24 ways.

(iv) All vowels come together

There are 2 vowels which are O ,E.

Consider this group.

Therefore, the permutation of 5 groups is 5! = 120

The group of vowels can also be arranged in 2! = 2 ways.

Hence the total number of words in which vowels come together are 120×2 = 240 words.

(v) All consonants come together

There are 4 consonants V,W,L,S. consider this a group.

Therefore, a permutation of 3 groups is 3! = 6 ways.

The group of consonants also can be arranged in 4! = 24 ways.

Hence, the total number of words in which consonants come together is 6×24 = 144 words.