Question

How many different words can be formed from the letters of the word GANESHPURI when:
The vowels are always together.

Answer 1

GANESHPURI: No. of letters $=10$ vevels are AEUI i.e. 4 and consonants 6.

The four vowels AEUI are to be together. Take these four letters as one letter and so we can have in all $10-4+1=7$ letters which can be arranged in $7$! ways. In each of these $7$! arrangements the four vowels are together and these can be arranged amongst themselves in $4$! ways. Hence by fundamental theorem the number of words will be $7!.4!$ in which the vowels will be together.