Two cards are drawn at random from a well-shuffled pack of $52$ cards. Find the probability that one card is a prime number and the other is a multiple of $5$.

Four cards are drawn at random from a pack of $52$ playing cards. What is the probability that one card is drawn from each suit?

From a group of $7$ men and $4$ ladies,a committee of $6$ persons is formed. What is the probability that the committee contains exactly $2$ ladies?

$A$ box contains $50$ tickets numbered $1, 2, 3, \dots, 50$. Five tickets are drawn at random and arranged in ascending order $(x_1 < x_2 < x_3 < x_4 < x_5)$. What is the probability that $x_3 = 30$?

Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$.
Statement-$1$: The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{85}$.
Statement-$2$: If the four chosen numbers form an $A.P.$,then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

If a person throws $3$ dice,what is the probability that the sum of the numbers obtained is exactly $15$?