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

$n$-digit numbers are formed using only three digits $2, 5$,and $7$. The smallest value of $n$ for which $900$ such distinct numbers can be formed is:

Six married couples decide to form a committee of $6$ persons. The total number of ways to form the committee such that it contains no couples is equal to:

The students in a class are seated according to their marks in the previous examination. Once,it so happens that four of the students got equal marks and therefore the same rank. To decide their seating arrangement,the teacher wants to write down all possible arrangements,one in each of separate bits of paper,in order to choose one of these by lots. How many bits of paper are required?

In how many ways can $5$ boys and $5$ girls sit in a circle so that no two boys sit together?

If all the words,with or without meaning,are written using the letters of the word $QUEEN$ and are arranged as in an English dictionary,then the position of the word $QUEEN$ is (in $^{th}$)