2010 UNCO Math Contest II Problems/Problem 5

Revision as of 20:51, 9 February 2015 by Haradica (talk | contribs) (Solution)

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) Let us write the position of any coin as $(r,c)$. Then, $0 \le r \le 3, 0 \le c \le 3$. Therefore, there are $4 \times 4 = 16$ different positions for the first coin, and $3 \times 3 = 9$ possibilities for the second coin. Together, there are $16 \times 9 = 144$ possible placements of the two coins.

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