$A$ bag contains $3$ red,$4$ white,and $5$ black balls. If three balls are drawn at random,what is the probability that they are of different colors?

An urn contains nine balls of which three are red,four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

$A$ die marked with digits $\{1, 2, 2, 3, 3, 3\}$ is thrown three times. The probability of getting a sum of $6$ on the faces of the die is equal to:

There are $8$ boys and $7$ girls in a classroom. If the names of all those children are written on paper slips and $3$ slips are drawn at random from them,then the probability of getting the names of one boy and two girls or one girl and two boys is