(Q). Consider three set of parallel lines in a plane containing ‘x’, ‘y’, ‘z’ parallel lines respectively. What is the highest number of parallelograms that can be formed with these set of parallel lines?
Solution:-
Consider pair of parallel lines from ‘x’ and ‘y’ parallel lines. First we will select 2 lines from ‘x’ straight lines and 2 lines from ‘y’ straight lines, this can be done in ˣC₂×ʸC₂ ways.
Similarly, we can select pair from ‘y’ & ‘z’ straight lines & another pair from ‘z’ & ‘x’ straight lines. This can be done in ʸC₂×ᶻC₂ + ᶻC₂×ˣC₂ ways.
So total such parallelogram is
= ˣC₂×ʸC₂ + ʸC₂×ᶻC₂ + ᶻC₂×ˣC₂ Answer
