In how many ways can $10$ people be seated in $2$ boats such that each boat has $5$ people and two specific people do not sit in the same boat?

Determine the number of $5$-card combinations out of a deck of $52$ cards if each selection of $5$ cards has exactly one king.

$^{n-1}C_3 + ^{n-1}C_4 > ^nC_3$,then the value of $n$ is

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

In a Mathematics examination,there are $20$ questions of equal marks. The question paper is divided into three sections: $A, B$,and $C$. $A$ student is required to attempt a total of $15$ questions,taking at least $4$ questions from each section. If section $A$ has $8$ questions,section $B$ has $6$ questions,and section $C$ has $6$ questions,then the total number of ways a student can select $15$ questions is: