SATHEE: Permutations And Combinations Question 363

Permutations And Combinations Question 363

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:

[a] 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. therefor 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. $

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Permutations And Combinations Question 363

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