What is the number of diagonals in an octagon?

If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

Four distinct numbers are randomly selected out of the set of first $20$ natural numbers. The probability that no two of them are consecutive is -

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

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

Three of the six vertices of a regular hexagon are chosen at random. The probability that the triangle formed by these three vertices is equilateral is equal to