#Combinatorics and Counting # Permutations and Combinations

Question

1. If each of ‘a’ points on a straight line is joined to each of ‘b’ points on another straight line, excluding the points on the given two lines,then which of the following represents the number of points of intersection of these lines? Select all that apply.

1. (ab(a-1)(b-1))/4 
2. (ab(a-1)(b-1))/2
3. ab
4. C(a,2) * C(b,2)

Answer 1

option a and d

the only way to guarantee an intersection is to select any 2 points from line 1 and any 2 points from line 2.

thus, no. of ways to do the above operation is C(a,2) * C(b,2).

and

option d ↔ option a