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 the papers of $4$ students can be checked by any one of $7$ teachers,then the probability that all the $4$ papers are checked by exactly $2$ teachers is (in $/49$)

What is the probability that the sum of two numbers chosen at random from $40$ consecutive natural numbers is odd?

Two friends $A$ and $B$ have an equal number of daughters. There are three cinema tickets which are to be distributed among the daughters of $A$ and $B$. The probability that all the tickets go to the daughters of $A$ is $1/20$. The number of daughters each of them has is:

If Mohan has $3$ tickets of a lottery containing $3$ prizes and $9$ blanks,then his chance of winning at least one prize is

$A$ coin is tossed $2n$ times. The chance that the number of times one gets head is not equal to the number of times one gets tail is