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 six students,including two particular students $A$ and $B,$ stand in a row,then the probability that $A$ and $B$ are separated with one student in between them is

From $80$ cards numbered $1$ to $80$,two cards are selected randomly. The probability that both the cards have numbers divisible by $4$ is given by

If $6$ girls and $5$ boys are sitting in a row,what is the probability that no two boys sit together?

Out of $21$ tickets marked with numbers from $1$ to $21$,three are drawn at random. The chance that the numbers on them are in $A.P.$ 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?