Question

How many straight lines can be formed by joining 12 points on a plane out of which no points are collinear?

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Answer 1

hey mate here is ur answer

12C2 lines are formed

answer is 66

Answer 2

Given :

Number of points on a plane =12

No points are collinear

To find :

Number of straight lines

Solution :

The number of points on a plane are 12.

For making a line, we have to choose minimum 2 points at once.

It is given that no points are collinear.It means

for making a line, we have to choose any combination of two points.

The formula of choosing r points out of n points as a combination is =

$\bf \binom{n}{r} = \: ^{n}c _r \: = \frac{n!}{r!(n - r)!}$

As we have to choose combination of 2 points out of 12 points.

n =12 and r = 2

Putting in above formula

$\bf \binom{12}{2} = ^{12}c _2\: = \frac{12!}{2!(12 - 2)!} = ^{12}c _2= \frac{12!}{2!(10)!}$

So

The number of lines made by given situation is =

$\\ \\ \bf\frac{12 \times 11}{2 \times 1} = 66$

So, the number of lines = 66