Difference between revisions of "2010 AMC 10A Problems/Problem 22"
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<math>\textbf{(A)}\ 28 \qquad \textbf{(B)}\ 56 \qquad \textbf{(C)}\ 70 \qquad \textbf{(D)}\ 84 \qquad \textbf{(E)}\ 140</math> | <math>\textbf{(A)}\ 28 \qquad \textbf{(B)}\ 56 \qquad \textbf{(C)}\ 70 \qquad \textbf{(D)}\ 84 \qquad \textbf{(E)}\ 140</math> | ||
| + | ==Solution== | ||
To choose 3 points on a circle with 8 points, we simply have <math>{{8}\choose{3}}</math> to get the answer <math>\boxed{56}</math> | To choose 3 points on a circle with 8 points, we simply have <math>{{8}\choose{3}}</math> to get the answer <math>\boxed{56}</math> | ||
Revision as of 15:19, 20 December 2010
Problem
Eight points are chosen on a circle, and chords are drawn connecting every pair of points. No three chords intersect in a single point inside the circle. How many triangles with all three vertices in the interior of the circle are created?
Solution
To choose 3 points on a circle with 8 points, we simply have 
to get the answer 
