TS EAMCET · Maths · Permutation Combination
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 these points such that atleast one of the vertices of every triangle formed is from the given 4 collinear points is
- A 116
- B 96
- C 120
- D 100
Answer & Solution
Correct Answer
(B) 96
Step-by-step Solution
Detailed explanation
Required number of distinct triangles \[ \begin{aligned} & ={ }^4 C_1 \times{ }^6 C_2+{ }^4 C_2 \times{ }^6 C_1=4 \times \frac{6 \times 5}{2 \times 1}+\frac{4 \times 3}{2 \times 1} \times 6 \\ & =4 \times 3 \times 5+2 \times 3 \times 6=60+36=96 \end{aligned} \]
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