If a polygon of $n$ sides has $560$ diagonals,then $n=$

Two lines $l_1$ and $l_2$ intersect at a point $P$. If $A_1, B_1, C_1$ are points on $l_1$ and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and none of these points coincide with $P$,how many triangles can be formed using these $8$ points?

$A$ polygon has $35$ diagonals,then the number of its sides is

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

If a group of six students including two particular students $A$ and $B$ stand in a row,then the probability of getting an arrangement in which $A$ and $B$ are separated by exactly one student in between them is

There were two women participating in a chess tournament. Every participant played two games with every other participant. The number of games that the men played between themselves exceeded the number of games that the men played with the women by $66$. The total number of participants is