Question

Six straight lines are drawn in the plane such that no two lines are parallel and no three lines are concurrent. Then find the number of parts into which these lines divide the plane.

Answer 1

okay

so the first line intersects the lines at $6$ points

$2$ line intersects and creates $5$ points (as its intersection with the first line is already taken)

$3$ line intersects and creates 4 points

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$6$ line intersects and creates $0$ points but creates an extra plane

hence the number of parts the planes are divided is $1+1+2+3+.....+6=\sum 6$

that is equal to $22.$