If $6$ boys and $3$ girls are to be seated on $9$ chairs for a photograph,then the probability that the end seats are occupied by the girls and no two girls are side by side is

Fifteen persons,including $A$ and $B$,sit down at random at a round table. The probability that there are $4$ persons between $A$ and $B$ is

Let $m, n$ be two distinct integers chosen randomly from the set $\{0, 1, 2, \ldots, 99\}$. Then,the probability that $4^m + 4^n + 3$ is divisible by $5$ lies in the interval

Let $\omega$ be a complex cube root of unity with $\omega \neq 1$. $A$ fair die is thrown three times. If $r_1, r_2,$ and $r_3$ are the numbers obtained on the die,what is the probability that $\omega^{r_1} + \omega^{r_2} + \omega^{r_3} = 0$?

What is the probability of drawing two kings from a well-shuffled deck of $52$ cards?

The probability that a randomly chosen $5-digit$ number is made from exactly two digits is