If $6$ boys and $3$ girls are to be seated on $9$ chairs for a photograph,then the probability that the end seats are occupied by the girls and no two girls are side by side 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

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?

From a pack of $52$ cards,$3$ cards are drawn at random. Then,the probability that one is an ace,one is a queen,and one is a jack 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

Four cards are drawn at random from a pack of playing cards. The probability of getting exactly two cards from the same suit and the remaining two cards from two different suits is