$A$ bag contains $3$ red,$4$ white,and $5$ black balls. Three balls are drawn at random. The probability that they are of different colours is

Fifteen persons,including $A$ and $B$,sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

From a collection of eight cards numbered $1$ to $8$,if two cards are drawn at random,one after the other with replacement,then the probability that the product of the numbers that appear on the cards is a perfect square 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 $\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0$?

An urn contains $8$ red and $5$ white balls. Three balls are drawn at random. Then, the probability that balls of both colours are drawn is

$A$ bag contains $3$ red, $5$ black and $7$ blue balls. If three balls are drawn at random simultaneously from the bag, then the probability of getting at least two blue balls is