Manipal MET2013MathematicsPermutation and Combination
If m parallel lines in a plane are intersected by a family of n parallel lines, then the number of parallelograms that can be formed is
Options
- A1 4 m n(m-1)(n-1)
- B1 2 m n(m-1)(n-1)
- C1 4 m^2 n^2
- DNone of these
Correct answer
A. 1 4 m n(m-1)(n-1)
Step-by-step solution
Selection of 2 parallel lines from m= ^m C ₂ Selection of 2 parallel lines from n= ^n C₂ Hence, number of parallelograms = ^m C ₂ ^n C ₂= 1 4 (m-1)(n-1) m n