If the probability of getting $53$ Sundays and $53$ Mondays in a leap year is $\frac{x}{y}$, the greatest common factor of $x$ and $y$ is $1$, then find the value of $x+y$.

A bag contains $8$ red and $5$ white balls. Three balls are drawn at random. Find the probability that all the three balls are white.

A bag contains $8$ red and $5$white balls. Three balls are drawn at random. Find the probability that all the three balls are red.

A bag contains $8$ red and $5$white balls. Three balls are drawn at random. Find the probability that one ball is red and two balls are white.

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is a black king.

A card is drawn at random from a pack of$52$ cards. Find the probability that the card drawn is either a black card or a king.

A card is drawn at random from a pack of $52$ cards. Find the probability that the card drawn is black and a king.