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>
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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 01:47, 19 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?

$\textbf{(A)}\ 28 \qquad \textbf{(B)}\ 56 \qquad \textbf{(C)}\ 70 \qquad \textbf{(D)}\ 84 \qquad \textbf{(E)}\ 140$

To choose 3 points on a circle with 8 points, we simply have ${{8}\choose{3}}$ to get the answer $\boxed{56}$