The total number of three-digit numbers,where exactly one digit is repeated two times,is

In how many ways can $3$ letters be posted in $4$ letter boxes,if all the letters are not posted in the same letter box?

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

If $f(n) = n! (31-n)!$,where $n \in \{0, 1, 2, \ldots, 31\}$,then the minimum value of $f(n)$ is

$A$ question paper has $3$ parts and each part contains $4$ questions. The number of different ways in which a candidate can answer $8$ questions choosing at least two from each part is

Let $x$ denote the number of ways of arranging $m$ boys and $m$ girls in a row so that no two boys sit together. If $y$ and $z$ denote the number of ways of arranging $m$ boys and $m$ girls in a row and around a circular table respectively so that boys and girls sit alternately,then $x: y: z=$