# 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

• 62

•  63

• 64

•  65

#### 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