If ${ }^{n} C_{12}={ }^{n} C_{8}$,then $n$ is equal to

In how many ways can $12$ balls be distributed between two friends such that one gets $8$ balls and the other gets $4$ balls?

If $\frac{1}{{ }^{5}C_{r}} + \frac{1}{{ }^{6}C_{r}} = \frac{1}{{ }^{4}C_{r}},$ then the value of $r$ is

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?

The number of ways of forming a committee of $6$ members out of $5$ Indians,$5$ Americans,and $5$ Australians such that there will be at least one member from each country in the committee is:

The value of ${ }^{16} C_{9}+{ }^{16} C_{10}-{ }^{16} C_{6}-{ }^{16} C_{7}$ is