Number of ways in which the letters of the word W can be arranged if atleast one vowel is separated from rest of the vowels

Consider the word W = COMMISSIONER Find (i) Number of 5 letters word containing two vowels and three consonants. Number of ways in which all the letters of the word W can be arranged if alike letters are together but seperated from the other alike letters (iii) Number of ways in which letters of the word W can be arranged without changing order of alike letters.

The number of ways in which the letters of the word TRIANGLE can be arranged such that two vowels do not occur together is

Find the number of ways in which the letters of the word DRAUGHT can be arranged so that the vowels are always together .

Number of ways in which the letters of word GARDEN can be arranged with vowels in alphabetical order, is

The number of ways in which the letters of the word 'INSURANCE' be arranged so that the vowels are never separated is

The number of ways in which the letters of the word ALGEBRA can be arranged without changing the relative positions of Vowels and consonants is

The number of ways in which the letters of the word 'CONSTANT' can be arranged without changing the relative positions of the vowels and consonants is:

Find the number of ways in which the letters of the word 'INTERMEDIATE' can be arranged taken all at a time so that the vowels are not all together.