In a lottery,there are $90$ tickets numbered $1$ to $90$. If $5$ tickets are chosen at random,what is the probability that $2$ of the chosen tickets are $15$ and $89$?

Two persons $A$ and $B$ throw a pair of dice alternately until one of them gets the sum of the numbers appeared on the dice as $4$,and the person who gets this result first is declared as the winner. If $A$ starts the game,then the probability that $B$ wins the game is:

Four numbers are chosen at random from $\{1, 2, 3, \ldots, 40\}$. The probability that they are not consecutive is:

From a pack of $52$ playing cards,three cards are drawn simultaneously. The probability that these are one king,one queen,and one jack is:

Out of $13$ applicants for a job,there are $5$ women and $8$ men. It is desired to select $2$ persons for the job. The probability that at least one of the selected persons will be a woman is

If three distinct numbers are chosen randomly from the first $100$ natural numbers,then the probability that all three of them are divisible by both $2$ and $3$ is