What is the probability that a number formed using all the digits $1, 2, 3, 4, 5$ is divisible by $4$?

Two numbers are chosen at random from $\{1, 2, 3, 4, 5, 6, 7, 8\}$ at a time. The probability that the smaller of the two numbers is less than $4$ is

From a well-shuffled pack of $52$ cards,two cards are drawn at random. The probability that both cards are kings is:

$A$ five-digit number is formed by the digits $1, 2, 3, 4, 5$ with no digit being repeated. The probability that the number is divisible by $4$ is

Four boys and three girls stand in a queue for an interview. What is the probability that they will be in alternate positions?

Two numbers $b$ and $c$ are chosen at random in succession without replacement from the set $\{1, 2, 3, \ldots, 9\}$. Then the probability that $x^2 + bx + c > 0, \forall x \in R$ is