In how many ways can $10$ people line up at a ticket window of a cinema hall?

Let $T_n$ denote the number of triangles which can be formed using the vertices of a regular polygon of $n$ sides. If $T_{n + 1} - T_n = 21$,then $n$ equals:

How many numbers lying between $99$ and $1000$ can be formed using the digits $2, 3, 7, 0, 8, 6$,if each digit can be used only once in each number?

The number of ways in which $5$ boys and $3$ girls can be seated on a round table if a particular boy $B_1$ and a particular girl $G_1$ never sit adjacent to each other,is

There are $n$ points in a plane of which $p$ points are collinear. How many lines can be formed from these points?

There are $10$ points in a row. In how many ways can $4$ points be selected such that no two of them are consecutive?