Question

There are 10 points in a plane, out of these 6 are collinear, if n is the number of triangles formed by joining these points. then:

• A. $n\le 100$
• B. $100<n\le 140$
• C. $140<n\le 190$
• D. $n>190$

Answer 1

The correct option is A $n\le 100$

Number of required triangles:
${=}^{10}{C}_3{-}^6{C}_3$
$=\frac{10\times 9\times 8}{6}-\frac{6\times 5\times 4}{6}=120-20=100$