How many $6$-digit numbers can be formed using the digits of the number $112233$?

Using the digits $0, 2, 4, 6, 8$ not more than once in any number,the number of $5$-digit numbers that can be formed is:

Three persons enter a lift at the ground floor. The lift goes up to the $10^{\text{th}}$ floor. If the lift does not stop at the $1^{\text{st}}$, $2^{\text{nd}}$, and $3^{\text{rd}}$ floors, the number of ways in which the three persons can exit the lift at three different floors is equal to . . . . . . .

Compute $\frac{7!}{5!}$

How many numbers lying between $500$ and $600$ can be formed with the help of the digits $1, 2, 3, 4, 5, 6$ when the digits are not to be repeated?

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