In how many ways can the letters in the word GUWAHATI be arranged such that all the vowels are together

In how many ways can the letters of the words FRACTION be arranged so that the three vowels are never together?

In how many ways can the letters of the words PERMUTATIONS Vowels are together.

In how many ways can the letters of the words ALGEBRA be arranged in the form of words so that the two A's donot come together?

In how many ways can one post 3 letters in 5 post boxes?

In how many ways can the letters of the words DIRECTOR be arranged in the form of words so that the two R's do not come together?

In how many ways can the letters of the words PERMUTATIONS words start with P and end with S.

Find how many words can be formed of the letters of the words: FAILURE so that the vowels may never seperated.

Find how many words can be formed of the letters of the words: DAUGHTER so that the vowels may never seperated.

Find how many words can be formed of the letters of the words:COMBINE so that the vowels may never seperated.

There are 7 boys and 3 girls in a class. In how many ways can they be arranged in a row such that no two girls are together?