Difference between revisions of "2011 AMC 12A Problems/Problem 16"

(Created page with '== Problem == == Solution == == See also == {{AMC12 box|year=2011|num-b=15|num-a=17|ab=A}}')
 
(Problem)
Line 1: Line 1:
 
== Problem ==
 
== Problem ==
 +
Each vertex of convex polygon <math>ABCDE</math> is to be assigned a color. There are <math>6</math> colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?
 +
 +
<math>
 +
\textbf{(A)}\ 2520 \qquad
 +
\textbf{(B)}\ 2880 \qquad
 +
\textbf{(C)}\ 3120 \qquad
 +
\textbf{(D)}\ 3250 \qquad
 +
\textbf{(E)}\ 3750 </math>
 +
 
== Solution ==
 
== Solution ==
 
== See also ==
 
== See also ==
 
{{AMC12 box|year=2011|num-b=15|num-a=17|ab=A}}
 
{{AMC12 box|year=2011|num-b=15|num-a=17|ab=A}}

Revision as of 02:35, 10 February 2011

Problem

Each vertex of convex polygon $ABCDE$ is to be assigned a color. There are $6$ colors to choose from, and the ends of each diagonal must have different colors. How many different colorings are possible?

$\textbf{(A)}\ 2520 \qquad \textbf{(B)}\ 2880 \qquad \textbf{(C)}\ 3120 \qquad \textbf{(D)}\ 3250 \qquad \textbf{(E)}\ 3750$

Solution

See also

2011 AMC 12A (ProblemsAnswer KeyResources)
Preceded by
Problem 15
Followed by
Problem 17
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25
All AMC 12 Problems and Solutions
Invalid username
Login to AoPS