$A$ 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?

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 ————

$A$ box contains $9$ tickets numbered $1$ to $9$ both inclusive. If $3$ tickets are drawn from the box one at a time without replacement,then the probability that they are alternatively either {odd,even,odd} or {even,odd,even} is

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?

If two cards are drawn at random simultaneously from a well-shuffled pack of $52$ playing cards, then the probability of getting a card having a composite number and a card having a number which is a multiple of $3$ is

$A$ committee consists of $9$ experts taken from three institutions $A, B$,and $C$,of which $2$ are from $A$,$3$ from $B$,and $4$ from $C$. If three experts resign,then the probability that they belong to different institutions is