19. Show that n straight lines in the plane divide the plane into (n +n + 2)/2 regions. Assume that no two lines are parallel and that no three lines have a common point. 20. If n and r are integers such that 0 rn, let C(n,r) = n! / (r! (n-r)!). n! denotes the product no(n-1) (n-2)...... 3.2.1 and, by convention, 0! = 1. Show that C(n, 0) = 1 = C(n, n) and then, by mathematical induction, C(n, 0) + C(n, 1) + ... C(n, n) = 2^,