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The figure shows 5 points on one line and 4 points on another line parallel to it. How many triangles have all three corners among these 9 points?

Competition practicePermutations & Combinations

A84
B80
C70
D74

Step-by-Step Solution

All triples:

^{9} C_{3} = 84

. Three points from the same line make no triangle:

^{5} C_{3} +^{4} C_{3} = 10 + 4 = 14

. Triangles

= 84 - 14 = 70

.

Answer: C) 70

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