$A$ lock is made with $3$ rings,each marked with $10$ different letters. How many unsuccessful attempts can be made to open the lock?

In how many ways can $9$ examination papers be arranged so that the best and the worst papers are never together?

The number of $5$-letter words that can be formed by using the letters of the word $SARANAM$ is

All words,with or without meaning,are made using all the letters of the word $MONDAY$. These words are written as in a dictionary with serial numbers. The serial number of the word $MONDAY$ is

Three persons enter a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. If the lift does not stop at the $1^{\text{st}}$, $2^{\text{nd}}$, and $3^{\text{rd}}$ floors, the number of ways in which the three persons can exit the lift at three different floors is equal to . . . . . . .

$5$-digit numbers are to be formed using $2, 3, 5, 7, 9$ without repeating the digits. If $p$ is the number of such numbers that exceed $20000$ and $q$ is the number of those that lie between $30000$ and $90000$,then $p : q$ is