$n$ gentlemen can be made to sit on a round table in how many ways?

Out of $10$ white,$9$ black and $7$ red balls,the number of ways in which selection of one or more balls can be made,is

How many words can be formed using the letters of the word $INSURANCE$,such that all vowels always come together?

In how many ways can $5$ keys be put in a ring?

If the best and the worst paper never appear together,then six examination papers can be arranged in how many ways?

$A$ student is allowed to select at most $n$ books from a collection of $(2n + 1)$ books. If the total number of ways in which he can select at least one book is $63$,then the value of $n$ is