From a pack of $52$ cards,$3$ cards are drawn at random. Then,the probability that one is an ace,one is a queen,and one is a jack is

Four numbers are chosen at random (without replacement) from the set $\{1, 2, 3, ..., 20\}$.
Statement-$1$: The probability that the chosen numbers when arranged in some order will form an $A.P.$ is $\frac{1}{85}$.
Statement-$2$: If the four chosen numbers form an $A.P.$,then the set of all possible values of common difference is $\{\pm 1, \pm 2, \pm 3, \pm 4, \pm 5, \pm 6\}$.

Two numbers $a$ and $b$ are chosen at random from the set of the first $30$ natural numbers. The probability that $a^2 - b^2$ is divisible by $3$ is

Three squares of a chessboard are chosen at random. The probability that two are of one colour and one is of another colour 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 $12$ two-rupee coins,$7$ one-rupee coins,and $4$ fifty-paise coins. If three coins are selected at random,the probability that the sum of the values of the three coins is not an integral multiple of a rupee is: