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:

$A$ drawer contains $5$ brown socks and $4$ blue socks well mixed. $A$ man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match?

The numbers $2, 3, 5, 7, 11, 13$ are written on six distinct paper chits. If $3$ of them are chosen at random, then the probability that the sum of the numbers on the obtained chits is divisible by $3$ is:

$A$ box contains coupons labelled $1, 2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x_3 < x_4 < x_5$?

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 $5$.

Three numbers are chosen at random from numbers $1$ to $20$. The probability that they are consecutive is