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  • If a set of 6 parallel lines intersects 5 parallel lines, how many parallelograms can be formed?Option: 1 120<s

If a set of 6 parallel lines intersects 5 parallel lines, how many parallelograms can be formed?

Option: 1

120


Option: 2

140


Option: 3

170


Option: 4

150


Answers (1)

best_answer

Selecting two parallel lines from an intersection of eight parallel lines results in \mathrm{ { }^6 C_2}, which is multiplied by \mathrm{ ^5 C_2}, which is a selection of two parallel lines from another intersection of seven parallel lines.

The number of possible parallelograms from a set of 6 parallel lines intersecting 5 parallel lines is given by,

\mathrm{ { }^6 C_2 \times{ }^5 C_2=\frac{6 !}{2 ! 4 !} \times \frac{5 !}{2 ! 3 !} }

\mathrm{{ }^6 C_2 \times{ }^5 C_2=5 \times 6 \times 5 }

\mathrm{ { }^6 C_2 \times{ }^5 C_2=150}
Therefore, the number of ways the parallelogram is formed is 150 ways.

 

Posted by

shivangi.bhatnagar

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