Question

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 1

Answer: (B)

Required number of distinct triangles
$={}^4{C}_1\times {}^6{C}_2+{}^4{C}_2\times {}^6{C}_1=4\times \frac{6\times 5}{2\times 1}+\frac{4\times 3}{2\times 1}\times 6$
$=4\times 3\times 5+2\times 3\times 6=60+36=96$