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Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear. - Mathematics and Statistics

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Sum

Ten points are plotted on a plane. Find the number of straight lines obtained by joining these points if four points are collinear.

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Solution

To draw a line, two points are needed.
There are 10 points in a plane such that four points are collinear.
If no three of the given 10 points are collinear,
we will get 10C2 lines. But 4 points are collinear.
So, we will not get 4C2 lines from these points. Instead,
we get only one line containing the 4 points.
∴ Number of straight lines formed

= `""^10"C"_2 - ""^4"C"_2+1`

= `(10 xx 9)/2 + (4 xx 3)/2 + 1`

= 45 – 6 + 1
= 40
40 straight lines are obtained if four points are collinear.

Concept: Properties of Combinations
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APPEARS IN

Balbharati Mathematics and Statistics 2 (Commerce) 11th Standard HSC Maharashtra State Board
Chapter 6 Permutations and Combinations
Exercise 6.6 | Q 13. (ii) | Page 90
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