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

$A$ 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.

$A$ committee of $5$ is to be formed from a group of $9$ people. What is the probability that a specific married couple is either both included or both excluded from the committee?

In a collection of $10$ tickets,there are $2$ winning tickets. From this collection,$5$ tickets are drawn at random. Let $p_1$ and $p_2$ be the probabilities of obtaining $1$ and $2$ winning tickets,respectively. Then $p_1+p_2$ lies in the interval:

$A$ 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

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?