$A$ 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

Two cards are drawn at random from a standard pack of $52$ cards. The probability that the draw consists of exactly one face card and exactly one ace card is

Four cards are drawn one by one from a well-shuffled pack of $52$ cards. What is the probability that all four cards belong to the same suit?

Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

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 $3$?

$A$ bag contains $13$ red,$14$ green,and $15$ black balls. The probability of getting exactly $2$ black balls when pulling out $4$ balls is $P_1$. Now,the number of balls of each color is doubled,and $8$ balls are pulled out. The probability of getting exactly $4$ black balls is $P_2$. Then: