20
Part of 2003 AMC 12-AHSME
Problems(2)
15-Letter Arrangements
Source:
2/20/2008
How many -letter arrangements of A's, B's, and C's have no A's in the first letters, no B's in the next letters, and no C's in the last letters?
(A)\ \sum_{k\equal{}0}^5\binom{5}{k}^3 \qquad
(B)\ 3^5\cdot 2^5 \qquad
(C)\ 2^{15} \qquad
(D)\ \frac{15!}{(5!)^3} \qquad
(E)\ 3^{15}
countingdistinguishabilityAMC12
Cubic
Source:
1/5/2009
Part of the graph of f(x) \equal{} x^3 \plus{} bx^2 \plus{} cx \plus{} d is shown. What is ?
[asy]import graph;
unitsize(1.5cm);
defaultpen(linewidth(.8pt)+fontsize(8pt));
dotfactor=3;real y(real x)
{
return (x-1)*(x+1)*(x-2);
}path bounds=(-1.5,-1)--(1.5,-1)--(1.5,2.5)--(-1.5,2.5)--cycle;pair[] points={(-1,0),(0,2),(1,0)};
draw(bounds,white);
draw(graph(y,-1.5,1.5));
drawline((0,0),(1,0));
drawline((0,0),(0,1));
dot(points);
label("",(-1,0),SE);
label("",(1,0),SW);
label("",(0,2),NE);clip(bounds);[/asy] (A)\minus{}\!4 \qquad (B)\minus{}\!2 \qquad (C)\ 0 \qquad (D)\ 2 \qquad (E)\ 4