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?

$A$ box contains $6$ bottles of $V_1$ drink,$3$ bottles of $V_2$ drink and $4$ bottles of $V_3$ drink. If three bottles are drawn at random,then the probability that the three are not of the same variety is

Two points are randomly chosen on the circumference of a circle of radius $r$. The probability that the distance between the two points is at least $r$ is equal to

Let $A$ denote the event that a $6$-digit integer formed by $0, 1, 2, 3, 4, 5, 6$ without repetitions is divisible by $3$. Then the probability of event $A$ is equal to:

$A$ box contains $2$ black,$4$ white and $3$ red balls. One ball is drawn at random from the box and kept aside. From the remaining balls in the box,another ball is drawn at random and kept aside the first. This process is repeated until all the balls are drawn from the box. The probability that the balls drawn are in the sequence of $2$ black,$4$ white and $3$ red 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?