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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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Question

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

Sum
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Solution

There are 10 points on a plane.

When 4 of them are collinear

∴ Number of lines passing through these points if 4 points are collinear

= 10C24C2 + 1

= `45 - (4!)/(2!2!) + 1`

= `45 - (4 xx 3 xx 2!)/(2 xx 2!) + 1`

= 45 – 6 + 1

= 40

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Properties of Combinations
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Chapter 3: Permutations and Combination - Exercise 3.6 [Page 65]

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Balbharati Mathematics and Statistics 2 (Arts and Science) [English] Standard 11 Maharashtra State Board
Chapter 3 Permutations and Combination
Exercise 3.6 | Q 13. (b) | Page 65

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