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There Are 12 Points in a Plane. the Number of the Straight Lines Joining Any Two of Them When 3 of Them Are Collinear, is (A) 62 (B) 63 (C) 64 (D) 65 - Mathematics

MCQ

There are 12 points in a plane. The number of the straight lines joining any two of them when 3 of them are collinear, is

Options

  • 62

  •  63

  • 64

  •  65

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Solution

64
Number of straight lines joining 12 points if we take 2 points at a time = 12C2

\[= \frac{12!}{2! 10!} = 66\]
Number of straight lines joining 3 points if we take 2 points at a time = 3C2 = 3
But, 3 collinear points, when joined in pairs, give only one line.
∴ Required number of straight lines =\[66 - 3 + 1 = 64\]

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APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 17 Combinations
Q 12 | Page 25
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