MathDB

5

Part of 2004 AMC 10

Problems(2)

Problem: 2004 AMC 10 #5

Source:

2/1/2007
A set of three points is randomly chosen from the grid shown. Each three point set has the same probability of being chosen. What is the probability that the points lie on the same straight line? [asy]unitsize(.5cm); defaultpen(linewidth(.8pt)); dotfactor=3;
pair[] dotted={(0,0),(0,1),(0,2),(1,0),(1,1),(1,2),(2,0),(2,1),(2,2)};
dot(dotted);[/asy]<spanclass=′latex−bold′>(A)</span> 121<spanclass=′latex−bold′>(B)</span> 114<spanclass=′latex−bold′>(C)</span> 221<spanclass=′latex−bold′>(D)</span> 17<spanclass=′latex−bold′>(E)</span> 27 <span class='latex-bold'>(A)</span>\ \frac {1}{21}\qquad <span class='latex-bold'>(B)</span>\ \frac {1}{14}\qquad <span class='latex-bold'>(C)</span>\ \frac {2}{21}\qquad <span class='latex-bold'>(D)</span>\ \frac {1}{7}\qquad <span class='latex-bold'>(E)</span>\ \frac {2}{7}
probability
Maximizing Expression

Source:

1/5/2009
In the expression c\cdot a^b\minus{}d, the values of a a, b b, c c, and d d are 0 0, 1 1, 2 2, and 3 3, although not necessarily in that order. What is the maximum possible value of the result? <spanclass=′latex−bold′>(A)</span> 5<spanclass=′latex−bold′>(B)</span> 6<spanclass=′latex−bold′>(C)</span> 8<spanclass=′latex−bold′>(D)</span> 9<spanclass=′latex−bold′>(E)</span> 10 <span class='latex-bold'>(A)</span>\ 5\qquad <span class='latex-bold'>(B)</span>\ 6\qquad <span class='latex-bold'>(C)</span>\ 8\qquad <span class='latex-bold'>(D)</span>\ 9\qquad <span class='latex-bold'>(E)</span>\ 10