In how many ways can $5$ distinct balls be distributed among $3$ persons such that each person receives at least one ball?

If $n$ is an integer with $0 \leq n \leq 11$,then the minimum value of $n!(11-n)!$ is attained when a value of $n$ equals to

There are three sections in a question paper,each section containing $4$ questions. If a candidate has to answer exactly $5$ questions from this paper such that at least one question is answered from each section,then the number of ways in which a candidate can make the choice of questions is

The number of all five-letter words (with or without meaning) having at least one repeated letter that can be formed by using the letters of the word $INCONVENIENCE$ is:

The number of $4$-digit numbers that can be formed from the digits $0, 1, 2, 3, 4, 5, 6, 7$ such that each number contains the digit $1$ is:

The number of all possible combinations of $4$ letters which are taken from the letters of the word $ACCOMMODATION$ is