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:

Two numbers are selected at random from the first $40$ natural numbers. What is the probability that their sum is odd?

If $7$ identical white balls and $3$ identical black balls are arranged in a row at random,what is the probability that no two black balls are together?

If the papers of $4$ students can be checked by any one of $7$ teachers,then the probability that all the $4$ papers are checked by exactly $2$ teachers is (in $/49$)

If $4$ letters are selected at random from the letters of the word $PROBABILITY$, then the probability of getting a combination of letters in which at least one letter is repeated is