The units digit of $\sum\limits_{1 < p < 100} {p! - \sum\limits_{n = 1}^{50} {(2n)!} }$ is:

The domain of the function $f(x) = ^{16 - x}C_{2x - 1} + ^{20 - 3x}P_{4x - 5}$,where the symbols have their usual meanings,is the set

Find the remainder when $(1!)^2 + (2!)^2 + (3!)^2 + \dots + (100!)^2$ is divided by $10^2$.

If all the letters of the word $COMBINATION$ are arranged in all possible ways to form $11$ letter words (with or without meaning),then the number of words among them in which $C$ and $N$ occupy the end positions and no vowel appears exactly in the middle position is

Out of all possible $8$-digit numbers formed using all the digits $0, 0, 1, 1, 2, 3, 4, 4$,a number is randomly selected. The probability that the selected number is odd is:

$A$ building has a ground floor and $10$ more floors. Nine persons enter a lift at the ground floor. The lift goes up to the $10$th floor. The number of ways in which any $4$ persons exit at a floor and the remaining $5$ persons exit at a different floor, if the lift does not stop at the first and the second floors, is equal to: