Four cards are drawn at random from a pack of $52$ playing cards. The probability of getting all four cards of the same suit is

$A$ 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 $x_3 < x_4 < x_5$?

From the first $100$ natural numbers,two numbers $a$ and $b$ are selected randomly without replacement. If the probability that $a-b \ge 10$ is $\frac{m}{n}$,with $\gcd(m, n)=1$,then $m+n$ is equal to:

If three distinct numbers are selected from the first $100$ natural numbers,what is the probability that all selected numbers are divisible by both $2$ and $3$?

From a group of $10$ men and $5$ women,a four-member committee is to be formed such that it must contain at least one woman. The probability that the committee has more women than men is:

$A$ bag contains $a$ white and $b$ black balls. Two players $A$ and $B$ alternately draw a ball from the bag,replacing the ball each time after the draw,until one of them draws a white ball and wins the game. $A$ begins the game. If the probability of $A$ winning the game is three times that of $B$,then the ratio $a : b$ is