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There are 10 points in a plane, of which no three points are collinear except 4 . Then, the number of distinct triangles that can be formed by joining any three points of these ten points, such that at least one of the vertices of every triangle formed is from the given 4 collinear points is
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Verified Answer
The correct answer is:
$96$
Number of required triangles:
(Select 1 point from 4 collinear and 2 from remaining 6 ) OR (select 2 from collinear points \& 1 from remaining 6 )
$$
\begin{aligned}
& =\left({ }^4 C_1 \times{ }^6 C_2\right)+\left({ }^4 C_2 \times{ }^6 C_1\right) \\
& =(4 \times 15)+(6 \times 6)=96
\end{aligned}
$$
(Select 1 point from 4 collinear and 2 from remaining 6 ) OR (select 2 from collinear points \& 1 from remaining 6 )
$$
\begin{aligned}
& =\left({ }^4 C_1 \times{ }^6 C_2\right)+\left({ }^4 C_2 \times{ }^6 C_1\right) \\
& =(4 \times 15)+(6 \times 6)=96
\end{aligned}
$$
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