Permutation and Combination

There are 8 concyclic points such that no two lines joining two of these points are parallel and no three lines joining three of these points are concurrent. Find the number of point of intersections of these lines which lie inside the circle.

#Combinatorics #HelpMe! #MathProblem #Math

Easy Math Editor

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Comments

Choose 4 points out of these 8 points.You can form 2 intersecting lines out of these 4 points.Hence for every 4 points you get a point of intersection.Hence the total number of points of intersection = $\binom{8}{3}$

Shaswata Roy - 7 years, 7 months ago

Math	Appears as
Remember to wrap math in `\(` ... `\)` or `\[` ... `\]` to ensure proper formatting.
`2 \times 3`	$2 \times 3$
`2^{34}`	$2^{34}$
`a_{i-1}`	$a_{i-1}$
`\frac{2}{3}`	$\frac{2}{3}$
`\sqrt{2}`	$\sqrt{2}$
`\sum_{i=1}^3`	$\sum_{i=1}^3$
`\sin \theta`	$\sin \theta$
`\boxed{123}`	$\boxed{123}$