Three numbers are chosen at random from $1$ to $15$. The probability that no two numbers are consecutive is:

The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line,is:

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?

If three of the six vertices of a regular hexagon are chosen at random,then the probability that the triangle formed with these chosen vertices is equilateral is

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

There are $n$ distinct points on the circumference of a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then what is the value of $n$?