$A$ bag contains $5$ white and $3$ black balls. If two balls are drawn at random,what is the probability that one ball is white and the other is black?

If two numbers are chosen at random from $1, 2, 3, \dots, 100$ and multiplied,what is the probability that the product is divisible by $3$?

$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

Three numbers are chosen from $1$ to $30$. The probability that the minimum number is $10$ and the maximum number is $26$ is

$A$ bag contains $5$ blue and an unknown number $x$ of red balls. Two balls are drawn at random. If the probability of both of them being blue is $\frac{5}{14}$,then the value of $x$ is equal to

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: