2010 UNCO Math Contest II Problems/Problem 5

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

2010 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 4	Followed by Problem 6
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2010 UNCO Math Contest II Problems/Problem 5

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