$A$ polygon has $54$ diagonals. The number of sides of this polygon is

The number of ways in which $3$ boys and $2$ girls can sit on a bench so that no two boys are adjacent is . . . . . .

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

In how many ways can $5$ boys and $5$ girls be arranged in a row such that no two girls are together?

There are $10$ points on the line segment $AB$ excluding $A$ and $B$,and $8$ points on the line segment $AC$ excluding $A$ and $C$. The number of triangles formed using these $18$ points (excluding $A, B,$ and $C$) is:

There are $10$ points in a plane,out of which $4$ are collinear. How many straight lines can be formed by joining any two of these points?