Three distinct numbers are selected from the first $100$ natural numbers. The probability that all three numbers are divisible by both $2$ and $3$ is:

The probability of getting a sum of $16$ in a single throw with three dice is:

The numbers $2, 3, 5, 7, 11, 13$ are written on six distinct paper chits. If $3$ of them are chosen at random,then the probability that the sum of the numbers on the obtained chits is divisible by $3$ is:

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. $A$ fair die is thrown three times. If $r_1, r_2,$ and $r_3$ are the numbers obtained on the die,what is the probability that $\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0$?

$3$ 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

Nine balls are drawn simultaneously from a bag containing $5$ white and $7$ black balls. The probability of drawing $3$ white and $6$ black balls is: