$A$ polygon has $54$ diagonals. Then,the number of its sides is

There are $5$ points $P_1, P_2, P_3, P_4, P_5$ on the side $AB$,excluding $A$ and $B$,of a triangle $ABC$. Similarly,there are $6$ points $P_6, P_7, \ldots, P_{11}$ on the side $BC$ and $7$ points $P_{12}, P_{13}, \ldots, P_{18}$ on the side $CA$ of the triangle. The number of triangles that can be formed using the points $P_1, P_2, \ldots, P_{18}$ as vertices is:

$A$ polygon has $44$ diagonals. The number of its sides is

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

Two squares are chosen at random on a chessboard. The probability that they have a side in common is:

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them is equal to: