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 how many ways can a mixed doubles tennis game be arranged from $7$ married couples if no husband and wife are in the same game?

In a plane,there are $37$ straight lines,of which $13$ pass through point $A$ and $11$ pass through point $B$. Moreover,no three lines (apart from the lines passing through $A$ and $B$) pass through the same point,and no two lines are parallel. What is the number of points of intersection of the straight lines?

If $3$ squares are chosen at random from the $64$ squares of a chess board,then the probability that all of them lie along the same diagonal line is

Three numbers are chosen at random from $1$ to $15$. The probability that no two numbers are consecutive is:

There are $10$ points in a plane,of which no three points are collinear except $4$. Then,the number of distinct triangles that can be formed by joining any three points of these ten points,such that at least one of the vertices of every triangle formed is from the given $4$ collinear points is