In a touring cricket team,there are $16$ players in all,including $5$ bowlers and $2$ wicket-keepers. How many teams of $11$ players can be chosen from these,such that the team includes exactly $3$ bowlers and $1$ wicket-keeper?

The product of any $r$ consecutive natural numbers is always divisible by

An engineer is required to visit a factory for exactly $4$ days during the first $15$ days of every month,and it is mandatory that no two visits take place on consecutive days. The number of all possible ways in which such visits to the factory can be made by the engineer during $1-15$ June $2021$ is:

The solution set of $^{10}C_{x-1} > 2 \cdot ^{10}C_x$ is

$^nC_r + ^nC_{r-1}$ is equal to

There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?