The number of integers $n$ such that $100 \leq n \leq 999$ and $n$ contains at most two distinct digits is:

The number of $3$-$digit$ odd numbers,whose sum of digits is a multiple of $7$,is

The remainder obtained when $1! + 2! + 95!$ is divided by $15$ is

The total number of $5$-digit numbers, formed by using the digits $1, 2, 3, 5, 6, 7$ without repetition, which are multiples of $6$, is

Consider the following two statements:
$I.$ If $n$ is a composite number,then $n$ divides $(n-1)!$.
$II.$ There are infinitely many natural numbers $n$ such that $n^3+2n^2+n$ divides $n!$.

In a relay race there are five teams $A, B, C, D$ and $E$. What is the probability that $A, B$ and $C$ are the first three to finish (in any order)? (Assume that all finishing orders are equally likely.)