$A$ bag contains $6$ blue and $6$ green balls. Pairs of balls are drawn without replacement until the bag is empty. The probability that each drawn pair consists of one blue and one green ball is:

$\omega$ is a complex cube root of unity. When an unbiased die is thrown $3$ times, if $\beta_1, \beta_2, \beta_3$ are the numbers appeared on the die, then the probability that $\beta_1, \beta_2$ and $\beta_3$ satisfy $\omega^{\beta_1}+\omega^{\beta_2}=-\omega^{\beta_3}$ is

What is the probability of drawing two kings from a well-shuffled deck of $52$ cards?

If $6$ girls and $5$ boys are sitting in a row,what is the probability that no two boys sit together?

Two numbers $x$ and $y$ are chosen at random (without replacement) from the set $\{1, 2, 3, \dots, 1000\}$. The probability that $|x^4 - y^4|$ is divisible by $5$ is -

Two numbers $a$ and $b$ are chosen at random from the set of the first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is