In how many ways can $21$ English books and $19$ Hindi books be placed in a row so that no two Hindi books are together?

The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line,is:

There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the total number of triangles formed by joining these points,then $N=$

In how many ways can $5$ boys and $5$ girls stand in a row so that no two girls may be together?

Let $ABC$ be a triangle. Consider four points $p_1, p_2, p_3, p_4$ on the side $AB$, five points $p_5, p_6, p_7, p_8, p_9$ on the side $BC$, and four points $p_{10}, p_{11}, p_{12}, p_{13}$ on the side $AC$. None of these points is a vertex of the triangle $ABC$. The total number of pentagons that can be formed by taking all the vertices from the points $p_1, p_2, \ldots, p_{13}$ 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?