Out of $21$ tickets marked with numbers from $1$ to $21$,three are drawn at random. The chance that the numbers on them are in $A.P.$ is

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:

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:

Three numbers are chosen at random from $1$ to $20$. The probability that the sum of the three numbers is divisible by $3$ 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?

$A$ mapping is selected at random from the set of all the mappings of the set $A = \{1, 2, ..., n\}$ into itself. The probability that the mapping selected is an injection is