Question

There are 15 points in a plane no three of which are collinear find the number of triangles formed by joining them

Answer 1

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here is your answer

(i). If no three points out of 15 points lie on a line, then the number of lines is 15C2 as exactly one line is drawn through two points. Since 4 out of 15 points are collinear, they from only one line instead of 4C2 lines. Hence the number of lines gets decreased by 4C­2 -1. Hence the required number of lines

= 15C2 -(4C2 -1) = 105 -6 +1 = 100

(ii). A triangle is formed by joining 3 non-collinear points. So if the 15 points are all non-collinear, 15C3 triangles can be formed. But here 4 points lie on a line and form no triangle instead of 4C3. Thus the required number of triangles

= 15C3 -4C3 = 455 -4 = 451

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Answer 2

Answer:

The number of triangles formed by joining them is 451.

Step-by-step explanation:

(i). If no three of the fifteen points lie on a line, the number of lines is 15C2, because only one line is drawn through two points. Because four of the fifteen points are collinear, they are connected by a single line rather than four C2 lines. As a result, the number of lines is reduced by 4C2 -1. As a result, the required number of lines

= 15C2 -(4C2 -1) = 105 -6 +1 = 100

(ii). Three non-collinear points are joined to form a triangle. If all 15 of the points are non-collinear, 15C3 triangles can be formed. Instead of 4C3, 4 points lie on a line and form no triangle. As a result, the required number of triangles

= 15C3 -4C3 = 455 -4 = 451

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