If four persons are chosen at random from a group of $3$ men,$2$ women and $4$ children,then the probability that exactly two of them are children is:

If the letters of the word "$ASSASSINATION$" are arranged at random in a row,then the probability that no two $A$'s come together is equal to

$A$ 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:

Let $m, n$ be two distinct integers chosen randomly from the set $\{0, 1, 2, \ldots, 99\}$. Then,the probability that $4^m + 4^n + 3$ is divisible by $5$ lies in the interval

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 $3$ numbers are chosen from the first $15$ natural numbers,what is the probability that the numbers are in arithmetic progression?