Difference between revisions of "2010 UNCO Math Contest II Problems/Problem 5"

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== Solution ==
 
== Solution ==
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(a)  <math>\tfrac{6}{455}</math>
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(b) <math>\frac{n!}{\binom{n^2}{n}}</math>
  
 
== See also ==
 
== See also ==
{{UNC Math Contest box|year=2010|n=II|num-b=4|num-a=6}}
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{{UNCO Math Contest box|year=2010|n=II|num-b=4|num-a=6}}
  
 
[[Category:Introductory Combinatorics Problems]]
 
[[Category:Introductory Combinatorics Problems]]

Latest revision as of 01:51, 13 January 2019

Problem

(a) In the $4 \times 4$ grid shown, four coins are randomly placed in different squares. What is the probability that no two coins lie in the same row or column?

$\begin{tabular}{|c|c|c|c|} \hline &&& \\ \hline &&& \\ \hline &&& \\ \hline &&& \\ \hline \end{tabular}$

(b) Generalize this to an $N \times N$ grid.


Solution

(a) $\tfrac{6}{455}$

(b) $\frac{n!}{\binom{n^2}{n}}$

See also

2010 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 4
Followed by
Problem 6
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions