$n$ gentlemen can be made to sit on a round table in how many ways?

The digits $4, 5, 6, 7, 8$ are written in every possible order. The number of numbers greater than $56000$ is

$A$ person is permitted to select at least one and at most $n$ coins from a collection of $(2n + 1)$ distinct coins. If the total number of ways in which he can select coins is $255$,then $n$ equals

In how many ways can a committee consisting of $5$ men and $6$ women be formed from $8$ men and $10$ women?

Statement-$1$: The number of ways of distributing $10$ identical balls in $4$ distinct boxes such that no box is empty is $^9C_3$.
Statement-$2$: The number of ways of choosing any $3$ places from $9$ different places is $^9C_3$.

How many triangles can be drawn by using $9$ non-collinear points?