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in Permutations and combinations by (52.7k points)

Given distinct lines L1 , L2 , …, L1000 in which all lines of the form L4n , where n is a positive integer, are parallel to each other. All lines L4n−3, are concurrent at a point. The maximum number of the points of intersection of pairs of line from the complete set (L1 , L2 , …, L1000) is

(A) 437251

(B) 437250

(C) 437252

(D) 437200

1 Answer

+1 vote
by (46.6k points)
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Best answer

Correct option  (A) 437251

1000 lines intersects at 1000C2 = 499500 points but 250 lines are parallel here 250C2 = 31125 intersections are lost. Also, 250 lines are concurrent so 250C2 – 1 = 31124 more intersection lost.

So,

499500 – 31125 – 31124 = 437251

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