in Combinatory
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Ans:  211

in Combinatory
199 views

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@Amit Mehta If you carefully notice, the first straight line $(L=1)$ divides the plane into $2$ regions. Again, the 2nd  line intersects $1$ line, creating $2$ regions. The 3rd creates $3$ regions. This question basically asks the number of regions that $n$ lines divide a plane into. It is given by n

$L_n = \frac{n^2 + n +2}{2}$

The proper derivation is provided here: Number of Regions N Lines Divide Plane (cut-the-knot.org)

 

 

 

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“n straight lines separate the plane such that no 2 lines are parallel and no 3 lines pass through a common point”

$number\ of\ planes=\frac{\left ( n^{2} +n+2\right )}{2}$

$n=20$

$=\frac{\left ( 20^{2}+20+2 \right )}{2}$

$=211$

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Bro how you derived the formula can you explain
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no, I didn't but you may check

It's from Rosen
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