How many different words can be formed from the letter of the word 'GANESHPURI'? In how many of these words:
(i)the letter G always occupies the first place?
(ii) the letter P and I respectively occupy first and last place?
(iii) the vowels are always together?

(ii) If $P$ occupies first and $I$ occupies the last place so we have to arrange the remaining $8$ letters which can be done in $8!$           ways.

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