Find the probability that when a hand of $7$ cards is drawn from a well-shuffled deck of $52$ cards,it contains at least $3$ Kings.

Out of $15$ players,there are $8$ batsmen and $7$ bowlers. What is the probability of selecting a team of $6$ batsmen and $5$ bowlers?

$A$ box contains coupons labelled $1, 2, \ldots, 100$. Five coupons are picked at random one after another without replacement. Let the numbers on the coupons be $x_1, x_2, \ldots, x_5$. What is the probability that $x_1 > x_2 > x_3$ and $x_3 < x_4 < x_5$?

The coefficients $a, b, c$ in the quadratic equation $ax^2 + bx + c = 0$ are chosen from the set $\{1, 2, 3, 4, 5, 6\}$. If the probability of this equation having two distinct real roots is $p$,then $216p$ equals:

$A$ basket contains $12$ apples in which $3$ are rotten. If $3$ apples are drawn at random simultaneously from it,then the probability of getting at most one rotten apple is

Six cards are drawn simultaneously from a pack of playing cards. What is the probability that $3$ will be red and $3$ will be black?