How many $3$-digit numbers can be formed by using the digits $1$ to $9$ if no digit is repeated?

The range of the function $f(x) = {}^{7 - x}P_{x - 3}$ is

The number of natural numbers less than $1000$ in which no digit is repeated is

How many $5$ digit telephone numbers can be constructed using the digits $0$ to $9$,if each number starts with $67$ and no digit appears more than once?

Ten chairs are numbered as $1$ to $10$. Three women and two men wish to occupy one chair each. First,the women choose the chairs marked $1$ to $6$,then the men choose the chairs from the remaining. The number of possible ways is

The number of five-digit numbers,greater than $40000$ and divisible by $5$,which can be formed using the digits $0, 1, 3, 5, 7,$ and $9$ without repetition,is equal to: