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.)

Letters in the word $HULULULU$ are rearranged. The probability of all three $L$ being together is

Let $5$-digit numbers be constructed using the digits $0, 2, 3, 4, 7, 9$ with repetition allowed,and are arranged in ascending order with serial numbers. Then the serial number of the number $42923$ is $...............$.

Consider $4$ boxes,where each box contains $3$ red balls and $2$ blue balls. Assume that all $20$ balls are distinct. In how many different ways can $10$ balls be chosen from these $4$ boxes so that from each box at least one red ball and one blue ball are chosen?

The number of ordered pairs $(x, y)$ of integers such that their product $xy$ is a positive integer less than $100$ is:

The number of three-digit numbers $\overline{abc}$ such that the arithmetic mean of $b$ and $c$ is equal to the square of their geometric mean is