The number of circular permutations of $n$ different objects is

$A$ 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?

There are $(n + 1)$ white and $(n + 1)$ black balls,each set numbered $1$ to $(n + 1)$. The number of ways in which the balls can be arranged in a row so that the adjacent balls are of different colours is

In how many ways can $mn$ letters be posted in $n$ letter-boxes?

The number of triangles that can be formed by choosing the vertices from a set of $12$ points,seven of which lie on the same straight line,is

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is