Question

The number of triangles that can be formed by $5$ points in a line and $3$ points on a parallel line is?

• A. ${}^{8}C_3$
• B. ${}^{8}C_3–{}^{5}C_3$
• C. ${}^{8}C_3–{}^{5}C_3-1$
• D. None of these

Answer 1

The correct option is C

${}^{8}C_3–{}^{5}C_3-1$

Explanation for the correct answer:

We have a total of $8$ points here. The number of points we need to make a triangle is $3$

We can select $3$ non-collinear points out of $8$ points in${}^{8}C_3$ ways

We can deduct the collinear points in ${}^{5}C_3+{}^3{C}_3$

Therefore, the number of triangles formed out of $8$ points removing the possibility of selecting collinear points $={}^{8}C_3–{}^{5}C_3-{}^3{C}_3={}^{8}C_3–{}^{5}C_3-1$

Hence, option C is the correct answer.