Posted by **Nichole** on Wednesday, December 14, 2011 at 11:56pm.

There are nine points on a piece of paper. No three of the points are collinear. How many different triangles can be formed by using three of the nine points as vertices?

- math -
**MathMate**, Thursday, December 15, 2011 at 3:25am
Number of possible choices for the first point = 9.

Number of possible choices for the second point = 8.

Number of possible choices for the third point = 7.

Possible triangles with specific order of points = 9*8*7 = 504.

However, when we say triangle, we are not really concerned in which order the points are selected. So we have *over-counted* the number of triangles by 6, which is the number of ways to order three points.

The number of *distinct* triangles is therefore 504/6=84.

This number is mathematically called

9 choose 3, calculated by

9!/(3!(9-3)!) = 84

where 9! is factorial 9, = 9*8*7*...*2*1

## Answer this Question

## Related Questions

- geometry - Please help me to draw this figure four points that are not collinear...
- math - suppose n points are in space, no three are collinear and no four or are ...
- math - My son has been given the collinear problem below that has be stumped two...
- Math - explanation - This is an example in the text book. Using vectors, ...
- geometry - distint points a, b, c, d, e, and f are marked on a circle. How many ...
- Math - Three points D, E, and F are collinear. Is there only one plane that ...
- math - a triangle is a figure formed by three segments connecting three ...
- Calculus II - show that; given any three non-collinear points (x1,y1), (x2,y2...
- Geometry - Plese show how it is possible for two triangles to intersect in one ...
- math - Are three collinear points are always also coplanar points.