The lengths of $6$ line segments are $2, 3, 4, 5, 6, 7$ units respectively. The number of triangles that can be formed using these line segments is ......

In a regular $15$-sided polygon with all its diagonals drawn,a diagonal is chosen at random. The probability that it is neither a shortest diagonal nor a longest diagonal is

If $a, b, c, d$ are four distinct numbers chosen from the set $\{1, 2, 3, \ldots, 9\}$,then the minimum value of $\frac{a}{b} + \frac{c}{d}$ is

Three parallel straight lines $L_1, L_2$ and $L_3$ lie on the same plane. Consider $5$ points on $L_1, 7$ points on $L_2$ and $9$ points on $L_3$. Then the maximum possible number of triangles formed with vertices at these points is:

The number of straight lines that can be formed by joining $8$ points on a circle is:

Suppose $t_n$ is the number of triangles formed using the vertices of a regular polygon of $n$ sides. If $t_{n+1} = t_n + 28$,then $n =$