The letter of the word `$ASSASSIN$' are written down at random in a row. The probability that no two $S$ occur together is

If the probability that a randomly chosen $6$-digit number formed by using digits $1$ and $8$ only is a multiple of $21$ is $p$, then $96\;p$ is equal to

Let $n$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that all the girls stand consecutively in the queue. Let $m$ be the number of ways in which $5$ boys and $5$ girls can stand in a queue in such a way that exactly four girls stand consecutively in the queue. Then the value of $\frac{m}{n}$ is

If $4 \,-$ digit numbers greater than $5,000$ are randomly formed from the digits $0,\,1,\,3,\,5,$ and $7,$ what is the probability of forming a number divisible by $5$ when, the digits are repeated ?

If $10$ different balls are to be placed in $4$ distinct boxes at random, then the probability that two of these boxes contain exactly $2$ and $3$ balls is 

Seven white balls and three black balls are randomly placed in a row. The probability that no two black balls are placed adjacently equals