The probability that the three cards drawn from a pack of $52$ cards are all red is

Two cards are drawn at random from a well-shuffled pack of $52$ cards. Find the probability that one card is a prime number and the other is a multiple of $5$.

Cards are drawn one by one at random from a well-shuffled full pack of $52$ cards until two aces are obtained for the first time. If $N$ is the number of cards required to be drawn,then $P(N = n)$,where $2 \le n \le 50$,is

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

From a month of $31$ days,$3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$,where $a, b \in N$ and $\text{gcd}(a, b) = 1$,then $a + b$ is equal to ————

$A$ poker hand consists of $5$ cards drawn at random from a well-shuffled pack of $52$ cards. The probability that a poker hand consists of a pair and a triple of equal face values (for example,$2$ sevens and $3$ kings or $2$ aces and $3$ queens,etc.) is: