Factorials

Find the remainder when $X = 1! + 2! + 3! + \cdots + 100!$ is divided by $240$.

If $42 (^nP_2)=(^nP_4)$ then the value of n is

Choose the correct option for the remainder when X = 1! + 2! + 3! + ...........+ 100! is divided by 24

If n is an integer between 0 to 21, then find a value of n for which the value of $n!(21-n)!$ is  minimum