The smallest positive integer $n$,for which $n! < {\left( {\frac{{n + 1}}{2}} \right)^n}$ holds is

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

The number of triplets $(x, y, z)$,where $x, y, z$ are distinct non-negative integers satisfying $x+y+z=15$,is

The number of five-digit numbers that are divisible by $6$ which can be formed by choosing digits from $\{0, 1, 2, 3, 4, 5\}$,when repetition is allowed,is

The total number of numbers lying between $100$ and $1000$ that can be formed with the digits $1, 2, 3, 4, 5$,if the repetition of digits is not allowed and the numbers are divisible by either $3$ or $5$,is:

Let $a, b, c \in \mathbb{N}$ and $a+b+c=5$. Let $L$ and $M$ be the least and greatest values of $2^a 3^b 5^c$ respectively. Then $M-L=$