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What is the number of triangles that can be formed by choosing

Question

What is the number of triangles that can be formed by choosing the vertices from a set of $12$ points in a plane, seven of which lie on the same straight line?

185

175

115

105

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What is the number of triangles that can be formed by choosing the vertices from a set of

12

points in a plane, seven of which lie on the same straight line?

6 mins ago

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Text solutionVerified

Total no. of points

= 12

No. of points in same line

= 7

No. of triangles formed

=^{12} C_{3} -^{7} C_{3}

^{n} C_{r} = \frac{n !}{r ! ( n - r )!}

No. of triangles

= \frac{12 !}{3 ! 9 !} - \frac{7 !}{3 ! 4 !} = \frac{12 \times 11 \times 10}{3 \times 2} - \frac{7 \times 6 \times 5}{3 \times 2}

= 220 - 35

= 185

total triangles.

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Question Text	What is the number of triangles that can be formed by choosing the vertices from a set of $12$ points in a plane, seven of which lie on the same straight line?
Answer Type	Text solution:1
Upvotes	150