All possible $5$-digit numbers,each having $5$ distinct digits,are formed using the digits $\{1, 2, 3, 5, 6, 8\}$. Among them,the number of such numbers which are divisible by $3$ but not by $6$ is:

How many words can be formed using $3$ consonants and $2$ vowels from $5$ consonants and $4$ vowels?

Assuming that the balls of the same color are identical,find the number of ways to select one or more balls from $10$ white,$9$ green,and $7$ black balls.

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

From a group of $7$ batsmen and $6$ bowlers,$10$ players are to be chosen for a team,which should include at least $4$ batsmen and at least $4$ bowlers. One batsman and one bowler,who are the captain and vice-captain of the team respectively,must be included. The total number of ways such a selection can be made is:

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.)