If the letters of the word "$ASSASSINATION$" are arranged at random in a row,then the probability that no two $A$'s come together is equal to

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:

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?

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 $B$ have respectively $n + 1$ and $n$ coins which they toss simultaneously. Then the probability that $A$ will have more heads than $B$ 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