$12$ persons are to be arranged at a round table. If two particular persons among them are not to be side by side,the total number of arrangements is

How many $3$-letter words can be formed from the letters of the word '$EXPERTISE$',if repetition of letters is not allowed?

The number of words formed from the letters of the word $RAJASTHAN$ by taking all the letters at a time in which vowels are alternate is:

In an election there are $8$ candidates,out of which $5$ are to be chosen. If a voter may vote for any number of candidates but not greater than the number to be chosen,then in how many ways can a voter vote?

There are $6$ multiple choice questions in an examination. How many sequences of answers are possible,if the first $2$ questions have $3$ choices each,the next $2$ have $4$ choices each,and the last $2$ have $5$ choices each?

The letters of the word $MODESTY$ are written in all possible orders and these words are written out as in a dictionary,then the rank of the word $MODESTY$ is