Four cards are drawn at random from a pack of $52$ playing cards. The probability of getting all four cards of the same suit is

If two numbers $a$ and $b$ are chosen from the first $30$ natural numbers,what is the probability that $a^2 - b^2$ is divisible by $3$?

$4$ cards are drawn from a well-shuffled deck of $52$ cards. What is the probability of obtaining $3$ diamonds and $1$ spade?

Let $A$ and $B$ be two finite sets having $m$ and $n$ elements respectively such that $m \le n.$ $A$ mapping is selected at random from the set of all mappings from $A$ to $B$. The probability that the mapping selected is an injection 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:

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