N points lie on a circle. You draw lines connecting all the points to each other. These lines divide up the circle into a number of regions. How many regions is this? Assume that the points are scattered in such a way as to give the maximum number of regions for that N.

Accepted Solution

Answer:[tex]Number\,of\,regions=^nC_{4}+^nC_{2}+1[/tex]Step-by-step explanation:In the question,There are 'n' points on the circle.For making the maximum number of regions we can do that by selecting 2 points from the given number of points.i.e. [tex]^nC_{2}[/tex]And,By selecting 4 points from the given number of points we get the extra regions formed on the intersection of the chords with each other.i.e. [tex]^nC_{4}[/tex]And, 1 more region.So, we can write it as,[tex]Number\,of\,regions=^nC_{4}+^nC_{2}+1[/tex]Therefore, the number of regions formed from the 'N' points are,[tex]^nC_{4}+^nC_{2}+1[/tex]