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Byju's Answer

Standard XII

Mathematics

Combination Based on Geometry

Ina plane, th...

Question

Ina plane, there are $37$ straight lines of which $13$ pass though point $A$ and $11$ passes through point $B$ . Besides, no three lines pass through one point no line passes through both lines points $A$ and $B$ , and no two are parallel. Find the number of points of intersection of the straight lines?

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Solution

The number of points of intersection of $37$ lines is $37 C_{2}$ .But $13$ straight lines out of the given $37$ straight lines pass through the same point $A$ .

Therefore instead of getting $^{13} C_{2}$ points,we get only one point A.Similarly $11$ straight lines out of the given $37$ straight lines intersect at point $B$ .Therefore instead of getting $11 C_{2}$ points,we get only one point $B$ .

Hence the number of intersection points of the lines is $^{37} C_{2} -^{13} C_{2} -^{11} C_{2} + 2 = 535$

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