Three cards are drawn at random from a pack of $52$ cards. What is the probability of drawing three aces?

If the coefficients $a$ and $b$ of a quadratic expression $x^2+ax+b$ are chosen from the sets $A=\{3, 4, 5\}$ and $B=\{1, 2, 3, 4\}$ respectively, then the probability that the equation $x^2+ax+b=0$ has real roots is

If $3$ numbers are chosen from the first $15$ natural numbers,what is the probability that the numbers are in arithmetic progression?

Three numbers are chosen at random from numbers $1$ to $20$. The probability that they are consecutive is

Two different families $A$ and $B$ are blessed with an equal number of children. There are $3$ tickets to be distributed amongst the children of these families so that no child gets more than one ticket. If the probability that all the tickets go to the children of family $B$ is $\frac{1}{12}$,then the number of children in each family is?

Two cards are drawn at random from a well-shuffled pack of $52$ cards. Find the probability that one card is a prime number and the other is a multiple of $5$.