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 $4$-digit numbers greater than $5,000$ are randomly formed from the digits $0, 1, 3, 5,$ and $7$,what is the probability of forming a number divisible by $5$ when the digits are repeated?

The probability of forming a $12$-person committee from $4$ engineers,$2$ doctors,and $10$ professors containing at least $3$ engineers and at least $1$ doctor is:

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

$A$ bag contains $5$ red balls, $3$ black balls, and $4$ white balls. Three balls are drawn at random. The probability that they are not of the same colour is

$A$ committee of $9$ experts is formed from three organizations $A$,$B$,and $C$,consisting of $2$ from $A$,$3$ from $B$,and $4$ from $C$. If three experts resign,find the probability that they belong to different organizations.