There are $9$ balls to be placed in $9$ boxes. If $5$ of the balls cannot fit into $3$ specific small boxes,find the number of ways to arrange exactly one ball in each of the boxes.

How many numbers less than $1000$ can be formed using the digits $1, 2, 3, 4, 5, 6$ if repetition is not allowed?

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 . . . . . . .

There are $10$ distinct letters of the English alphabet. Words of $5$ letters are formed using these letters. How many such words can be formed if at least one letter is repeated?

How many words can be formed using the letters of the word $SCHOLAR$ that start with $A$ and end with $S$?

The number of distinct positive integers that can be formed using $0, 1, 2, 3$,where each integer is used at most once,is equal to