Using principles of Permutations and Combinations solve this problem.?

Question

Each of a set of 6 parallel lines cuts each one of another set of 5 parallel lines.Find which of the following numbers gives the correct number of different parallelograms so formed--60,120,150.

PLEASE PROVIDE SOLUTIONS TO JUSTIFY YOUR ANSWER AND USE ONLY THE PRINCIPLES OF PERMUTATIONS AND COMBINATIONS.NO OTHER METHOD IS ALLOWED EXCEPT FOR PERMUTATIONS AND COMBINATIONS.

Answer 1

see in a ||gm we need two || lines in a opposite side so we chose 2 out of 6
i.e, 6C2

and two more || lines for other side then we have to chose 2 out of 5
i.e, 5C2

total cases 6C2 * 5C2

which will gives you
(6*5*4*3*2*1/2*1*4*3*2*1) * (5*4*3*2*1/2*1*3*2*1)
(15)*(10)
150

Answer 2

What makes up a parallelogram? Two pairs of parallel sides. So we need to choose two of the first set, and two of the second set, in 6C2 * 5C2 = 150 ways.