Two cards are drawn from a pack of $52$ cards. What is the probability that at least one of the cards drawn is an ace?

All the spades are taken out from a pack of cards. From these cards,cards are drawn one by one without replacement until the ace of spades comes. The probability that the ace of spades comes in the $4^{th}$ draw is

Out of $3$ men,$2$ women,and $4$ children,if $4$ people are selected at random,what is the probability that exactly $2$ children are selected?

Two distinct numbers $a$ and $b$ are selected at random from ${1, 2, 3, \dots, 50}$. The probability that their product $ab$ is divisible by $3$ is:

$A$ basket contains $3$ mangoes and $3$ apples. If two fruits are selected at random,what is the probability of getting one mango and one apple?

Out of the first $5$ consecutive natural numbers,if two different numbers $x$ and $y$ are chosen at random,then the probability that $x^4 - y^4$ is divisible by $5$ is