Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?

$A$ 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

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

$4$ boys and $2$ girls occupy seats in a row at random. The probability that the two girls occupy seats side by side is:

Let $S$ be the set of all the words that can be formed by arranging all the letters of the word $\text{GARDEN}$. From the set $S$,one word is selected at random. The probability that the selected word will $\text{NOT}$ have vowels in alphabetical order is:

$A$ group of $3$ is selected at random from $3$ men,$2$ women,and $4$ children. What is the probability that the group contains exactly $2$ children?