Will you count quadrilaterals?

Probability Level 3

How many quadrilaterals can be obtained from 5 straight lines (parallel to each other) and 6 straight lines (parallel to each other) crossing each other (See the figure)?


The answer is 150.

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Sahil Silare by Sahil Silare , 20, India

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1 solution

Richard Costen
Sep 27, 2016

All of the possible quadrilaterals can be chosen by choosing all possibilities of any 2 lines from the 5 horizontal parallel lines, and any 2 lines from the 6 other parallel lines crossing them. This can be represented by: ( 5 2 ) × ( 6 2 ) = 10 × 15 = 150 {5 \choose 2} \times {6 \choose 2} = 10 \times 15 = \boxed{150}

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