Six boys and six girls sit in a row. What is the probability that the boys and girls sit alternatively?

$3$ balls are drawn one after the other without replacement from an urn containing $4$ red, $5$ blue and $6$ yellow balls. The probability of getting three different coloured balls is

In a box,there are $2$ red,$3$ black,and $4$ white balls. If $3$ balls are drawn together,what is the probability that they are of the same color?

$A$ bag contains $8$ red and $7$ black balls. Two balls are drawn at random. The probability that both the balls are of the same colour is

From $3n$ consecutive integers, three integers are selected at random. The probability that their sum is divisible by $3$ 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