$A$ 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?

Nine balls are drawn simultaneously from a bag containing $5$ white and $7$ black balls. The probability of drawing $3$ white and $6$ black balls is:

If a coin is tossed seven times, then the probability of getting exactly three heads such that no two heads occur consecutively is

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:

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?

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: