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

Assuming the balls to be identical except for their color,the number of ways in which one or more balls can be selected from $10$ white,$9$ green,and $7$ black balls is:

If the number of seven-digit numbers,such that the sum of their digits is even,is $m \cdot n \cdot 10^{n}$; $m, n \in \{1, 2, 3, \ldots, 9\}$,then $m+n$ is equal to . . . . . . .

The number of ways of selecting two numbers $a$ and $b$,where $a \in \{2, 4, 6, \ldots, 100\}$ and $b \in \{1, 3, 5, \ldots, 99\}$,such that the remainder is $2$ when $a+b$ is divided by $23$ is:

The number of four-digit natural numbers which contain exactly two distinct digits is:

Numbers between $1$ and $10,000$ are formed using the digits $2$ and $3$ exactly once and the digit $4$ twice. If the numbers thus formed are arranged in increasing order and $x, y$ represent the ranks of $4324$ and $324$ respectively,then $x-y=$