First slide

Combinations

Question

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

Moderate

A

$^{8} C_{3}$
B

$^{8} C_{3} -^{5} C_{3}$
C

$^{8} C_{3} -^{5} C_{3} - 1$
D

None of these

Solution

The triangle will be formed by joining any three non-collinear points.
Required number of ways
$\begin{array}{l} =^{8} C_{3} -^{5} C_{3} -^{3} C_{3} \\ =^{8} C_{3} -^{5} C_{3} - 1 \end{array}$

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