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how many triangles

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by beater » Thu Jan 15, 2009 12:31 pm
If one of two parallel lines has 7 points on it and the other has 8, how many triangles can be drawn using the points?

a. 168
b. 196
c. 316
d. 364
e. 455
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by sachinkr » Thu Jan 15, 2009 1:20 pm
Line A - 7 Points
Line B - 8 Points

A triangle can be drawn by either taking 2 points in line A & 1 point in Line B or 2 points in Line B & 1 Point in Line B.

2 Points in Line A & 1 Point in Line B

= No of ways of getting 2 points from Line A * No of ways of getting 1 point from Line B
= 7C2 * 8 = 168

2 Points in Line B & 1 Point in Line A

= No of ways of getting 2 points from Line B * No of ways of getting 1 point from Line A
= 8C2 * 7 = 196

Total no of triangles = 168 + 196 = 364.
Ans (D)
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