If three cards are drawn randomly from a pack of $52$ playing cards, then the probability of getting exactly one spade card, exactly one king, and exactly one card having a prime number is

If three letters can be posted to any one of the $5$ different addresses,then the probability that the three letters are posted to exactly two addresses is:

Two numbers are selected at random from the numbers $1, 2, \dots, n$. The probability that the difference between the first and second number is not less than $m$ (where $0 < m < n$) 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 $5$.

In a consignment of $15$ articles,it is found that $3$ are defective. If a sample of $5$ articles is chosen at random from it,then the probability of having $2$ defective articles is

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is