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12 Oct 2021, 04:15
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Difficulty:
85%
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Question Stats:
38% (02:07) correct
62%
(02:42)
wrong
based on 61
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24 lines are drawn in a plane. Of these, 8 lines pass through point A and 11 lines pass through point B. No other three lines pass through the same point. Also, no line passes through both the points A and B and no two lines are parallel. Including A and B, what is the total number of points of intersections among the 24 lines?
A. 105
B. 193
C. 195
D. 257
E. 276
A. 105
B. 193
C. 195
D. 257
E. 276
13 Oct 2021, 04:29
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Let the lines that intersect line A be A. A = 11
Let the lines that intersect line B be B: B = 8
Let the remaining 5 lines be C
Number of intersections between A and B: 11*8 = 88
Number of intersections between A and C: 11*5 = 55
Number of intersections between B and C: 8*5 = 40
Lines from C which intersect: 5!/2!3! = 5*4/2 = 10
A and B are intersections = 2
88 + 55 + 40 + 10 + 2 = 195
Answer C
Let the lines that intersect line B be B: B = 8
Let the remaining 5 lines be C
Number of intersections between A and B: 11*8 = 88
Number of intersections between A and C: 11*5 = 55
Number of intersections between B and C: 8*5 = 40
Lines from C which intersect: 5!/2!3! = 5*4/2 = 10
A and B are intersections = 2
88 + 55 + 40 + 10 + 2 = 195
Answer C
03 Nov 2021, 07:52
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