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?

If the sides $AB, BC$ and $CA$ of a triangle $ABC$ have $3, 5$ and $6$ interior points respectively,then the total number of triangles that can be constructed using these points as vertices is equal to ....... .

Statement-$1$: If a polygon has $45$ diagonals,then the number of sides is $10$. Statement-$2$: Out of $n$ non-collinear points,$2$ points can be selected in $^nC_2$ ways.

Out of $30$ points in a plane,$8$ of them are collinear. The number of straight lines that can be formed by joining these points is:

$A$ rectangle with side lengths $2m - 1$ and $2n - 1$ is divided into unit squares by drawing parallel lines as shown. How many rectangles are there such that both side lengths are odd?

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the octagon is