There are two parallel lines with 6 points on one line and 8 points on the other. How many quadrilaterals can be formed by joining points on the two lines?

  • Option 1)

    210

  • Option 2)

    205

  • Option 3)

    418

  • Option 4)

    420

 

Answers (1)

as learnt in

Rule of Geometrical Permutations -

There are n points in a plane such that no three of them are in the same straight line then the number of lines that can be formed by joining is/are ^{n}c_{2} and number of triangle is/are ^{n}c_{3}.

-

 

 

To form a quadrilateral we need two points from each line. 

We get, 

^{6}C_{2} \times ^{8}C_{2}= \frac{6 \times 5}{2} \times \frac{ 8 \times 7}{2}

=15 \times 28=420


Option 1)

210

This option is incorrect.

Option 2)

205

This option is incorrect.

Option 3)

418

This option is incorrect.

Option 4)

420

This option is correct.

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