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KEAM 2013 Math Paper

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Question : 29 of 120

Marks: +1, -0

Choose 3, 4, 5 points other than vertices respectively on the sides AB, BC and CAo a triangle ABC. The number of triangles that can be formed using only these points as vertices is

220
217
215
210
205

Solution:

Required number of triangles that can be formed by using only given points as vertices

={}^{12}C_{3}-\{{}^{3}C_{3}+{}^{4}C_{3}+{}^{5}C_{3}\}

=\;\frac{12 \times 11 \times 10}{3 \times 2 \times 1}-\{1+4+\;\frac{5 \times 4}{2 \times 1}\}

=220-(5+10)

=220-15=205

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