The number of four-digit numbers strictly greater than $4321$ that can be formed using the digits $0, 1, 2, 3, 4, 5$ (repetition of digits is allowed) is

How many numbers between $5000$ and $10,000$ can be formed using the digits $1, 2, 3, 4, 5, 6, 7, 8, 9$ if each digit appears not more than once in each number?

In an examination hall,there are $4$ rows of chairs. Each row has $8$ chairs,$1$ behind the other. There are $2$ classes sitting for the examination with $16$ students in each class. It is desired that in each row,all students belong to the same class and that no $2$ adjacent rows are allotted to the same class. In how many ways can these $32$ students be seated?

How many $3$-digit numbers can be formed using $0, 2, 3, 5, 7$ when repetition is allowed?

The total number of numbers greater than $100$ and divisible by $5$,that can be formed from the digits $3, 4, 5, 6$,if no digit is repeated is:

If $^{n^2 - n}C_2 = ^{n^2 - n}C_{10}$,then $n = $