$5$ boys and $5$ girls are sitting in a row randomly. The probability that boys and girls sit alternatively is

If three letters can be posted to any one of the $5$ different addresses, then the probability that the three letters are posted to exactly two addresses is:

If an unbiased die, marked with $-2,-1,0,1,2,3$ on its faces, is through five times, then the probability that the product of the outcomes is positive, is :

Two numbers $x$ and $y$ are chosen at random from the set of integers $\{1,2,3,4......15\}.$ The probability that point $(x,y)$ lies on a line through $(0,0)$ having slope $\frac{2}{3}$ is

A bag contains $6$ white and $4$ black balls. A die is rolled once and the number of balls equal to the number obtained on the die are drawn from the bag at random. The probability that all the balls drawn are white is:

All face cards from pack of $52$ playing cards are removed. From remaining $40$ cards two are drawn randomly without replacement, then probability of drawing a pair (same denominations) is