If three distinct numbers are chosen randomly from the first $100$ natural numbers,then the probability that all three of them are divisible by both $2$ and $3$ is

$A$ box contains $12$ balls,of which $4$ are red,$5$ are green,and $3$ are white. If $3$ balls are drawn at random simultaneously from the box,then the probability that exactly $2$ balls have the same colour is

Two numbers are selected at random from the numbers $1, 2, \dots, n$. The probability that the difference between the first and second number is not less than $m$ (where $0 < m < n$) 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?

$A$ committee of $5$ is to be formed from a group of $9$ people. What is the probability that a specific married couple is either both included or both excluded from the committee?

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