For all $n \in N$,the product $(n+24)(n+25)(n+26)(n+27)$ is always divisible by:

From $6$ different novels and $3$ different dictionaries,$4$ novels and $1$ dictionary are to be selected and arranged in a row on a shelf so that the dictionary is always in the middle. The number of such arrangements is :

Find the number of natural number solutions to the equation $x_1 + x_2 = 100$,such that $x_1$ and $x_2$ are not multiples of $5$.

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

The number of four-letter words that can be formed using the letters of the word $BARRACK$ is

In how many ways can the letters of the word $ASSASSIN$ be arranged so that no two $S$s occur together?