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:

If $4$ cards are selected from a deck of $52$ cards,what is the probability that all cards are of the suit 'hearts'?

$A$ bag contains $8$ black and $7$ white balls. Two balls are drawn at random. For which outcome is the probability the highest?

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 three numbers are drawn at random successively without replacement from a set $S = \{1, 2, \ldots, 10\}$,then the probability that the minimum of the chosen numbers is $3$ or their maximum is $7$ is:

$A$ bag contains $12$ pairs of socks. If $4$ socks are picked up at random,the probability that there is at least one pair is equal to