MathDB

22

Part of 2010 AMC 10

Problems(2)

Interior Triangles

Source: AMC 10 2010A Problem 22

2/10/2010
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? <spanclass=′latex−bold′>(A)</span> 28<spanclass=′latex−bold′>(B)</span> 56<spanclass=′latex−bold′>(C)</span> 70<spanclass=′latex−bold′>(D)</span> 84<spanclass=′latex−bold′>(E)</span> 140 <span class='latex-bold'>(A)</span>\ 28 \qquad <span class='latex-bold'>(B)</span>\ 56 \qquad <span class='latex-bold'>(C)</span>\ 70 \qquad <span class='latex-bold'>(D)</span>\ 84 \qquad <span class='latex-bold'>(E)</span>\ 140
AMC
Distributing Candy

Source: 2010 AMC 10B Problem 22

2/26/2010
Seven distinct pieces of candy are to be distributed among three bags. The red bag and the blue bag must each receive at least one piece of candy; the white bag may remain empty. How many arrangements are possible? <spanclass=′latex−bold′>(A)</span> 1930<spanclass=′latex−bold′>(B)</span> 1931<spanclass=′latex−bold′>(C)</span> 1932<spanclass=′latex−bold′>(D)</span> 1933<spanclass=′latex−bold′>(E)</span> 1934 <span class='latex-bold'>(A)</span>\ 1930\qquad<span class='latex-bold'>(B)</span>\ 1931\qquad<span class='latex-bold'>(C)</span>\ 1932\qquad<span class='latex-bold'>(D)</span>\ 1933\qquad<span class='latex-bold'>(E)</span>\ 1934
AMC