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

From a month of $31$ days, $3$ different dates are selected at random. If the probability that these dates are in an increasing $A$.$P$. is equal to $\frac{a}{b}$, where $a, b \in N$ and $\text{gcd}(a, b) = 1$, then $a + b$ is equal to ————

Two persons $A$ and $B$ have respectively $n + 1$ and $n$ coins which they toss simultaneously. Then the probability that $A$ will have more heads than $B$ is

$A$ drawer contains $5$ brown socks and $4$ blue socks well mixed. $A$ man reaches the drawer and pulls out $2$ socks at random. What is the probability that they match?

The probability of forming a $12$-person committee from $4$ engineers,$2$ doctors,and $10$ professors containing at least $3$ engineers and at least $1$ doctor is:

$A$ committee has to be made of $5$ members from $6$ men and $4$ women. The probability that at least one woman is present in the committee is: