For a natural number $n$,the inequality $2^n(n - 1)! < n^n$ holds true if:

The total number of three-digit numbers,divisible by $3$,which can be formed using the digits $1, 3, 5, 8$,if repetition of digits is allowed,is:

If the $LCM$ of $p$ and $q$ is $r^2t^4s^2$,where $r, s,$ and $t$ are prime numbers,and $p$ and $q$ are positive integers,then the number of ordered pairs $(p, q)$ is ....

The number of numbers between $2000$ and $5000$ that can be formed with the digits $0, 1, 2, 3, 4$ (repetition of digits not allowed) and are multiples of $3$ is:

There are $15$ stations on a train route and the train has to be stopped at exactly $5$ stations among these $15$ stations. If it stops at at least two consecutive stations,then the number of ways in which the train can be stopped is

How many different words can be formed by jumbling the letters in the word $MISSISSIPPI$ in which no two $S$ are adjacent?