Question 20
$n$ is a positive integer. Let $A, B$ be two sets of $n$ points in the plane such that no three points of them are collinear. Denote by $T(A)$ the number of non-self-intersecting broken lines containing $n-1$ segments such that its vertices are in $A$. Define $T(B)$ similarly. If the elements of $B$ are the vertices of a convex $n$-gon but the elements of $A$ are not, prove that $T(B) \lt T(A)$.