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

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

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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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