First slide

Combinations

Question

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

Moderate

A

N > 190
B

$N \leq 100$
C

$100 < N \leq 140$
D

$140 < N \leq 190$

Solution

lf out of n points, m are collinear, then
Number of triangles = $^{n} C_{3} -^{m} C_{3}$
.'. Number of triangles = $^{10} C_{3} -^{6} C_{3} = 120 - 20 \Rightarrow N = 100$

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