Two integers are drawn at random from the set $\{5, 6, \ldots, 35\}$. What is the probability that their difference is odd?

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?

Two numbers are selected at random from the numbers $1, 2, \dots, n$. The probability that the difference between the first and second number is not less than $m$ (where $0 < m < n$) is

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains exactly $3$ Kings.

Let $X = \{(x, y) \in \mathbb{Z} \times \mathbb{Z} : \frac{x^2}{8} + \frac{y^2}{20} < 1 \text{ and } y^2 < 5x\}$. Three distinct points $P, Q,$ and $R$ are randomly chosen from $X$. Then the probability that $P, Q,$ and $R$ form a triangle whose area is a positive integer is

Two digits are selected randomly from the set $\{1, 2, 3, 4, 5, 6, 7, 8\}$ without replacement one by one. The probability that the minimum of the two digits is less than $5$ is