First slide

Combinations

Question

The number of triangles that are formed by choosing the vertices from a set of 12 points, seven of which lie on the same line is

Moderate

A

105
B

15
C

175
D

185

Solution

We know, a triangle will be formed by taking three points at a time.
.'.Required number of triangles $=^{12} C_{3} -^{7} C_{3}$
$= \frac{12 \times 11 \times 10}{3 \times 2 \times 1} - \frac{7 \times 6 \times 5}{3 \times 2} = 220 - 35 = 185$

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