If $^{n}C_{8} = ^{n}C_{2}$,find $^{n}C_{2}$.

If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

$A$ bag contains $5$ black and $6$ red balls. Determine the number of ways in which $2$ black and $3$ red balls can be selected.

$A$ country has $10$ smart cities. The government decides to connect all these cities by road. How many roads does the government need to construct so that every city is connected to every other city?

In a library,there are $n$ distinct books and each has $p$ copies. What is the number of ways to select one or more books?

In an election,there are $5$ candidates and $3$ vacancies. $A$ voter can vote for a maximum of $3$ candidates. In how many ways can a voter cast their vote?