The number of ways in which 6 men and 4 women can be seated around a table, so that a particular man and a particular woman never sit adjacent to each other is

The number of diagonals of a polygon is 35 . If $A$ and $B$ are two distinct vertices of this polygon, then the number of all those triangles formed by joining three vertices of the polygon having $A B$ as one of its sides 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

A student is asked to answer 10 out of 13 questions in an examination such that he must answer atleast four questions from the first five questions. Then, the total number of possible choices available to him is