Permutations And Combinations Question 71

Question: In a plane there are 37 straight lines of which 13 pass through the point $ A $ and 11 pass through the point $ B $ . Besides no three lines pass through one point, no line passes through both points $ A $ and $ B $ and no two are parallel. Then the number of intersection points the lines have is equal to

Options:

A) 535

B) 601

C) 728

D) None of these

Show Answer

Answer:

Correct Answer: A

Solution:

  • The number of points of intersection of 37 straight lines is $ ^{37}C_2 $ . But 13 of them pass through the point $ A $ . Therefore instead of getting $ ^{13}C_2 $ points we get merely one point. Similarly 11 straight lines out of the given 37 straight lines intersect at $ B $ . Therefore instead of getting $ ^{11}C_2 $ points, we get only one point. Hence the number of intersection points of the lines is $ ^{37}C_2{{-}^{13}}C_2{{-}^{11}}C_2+2=535 $ .