2010 UNCO Math Contest II Problems/Problem 5
Problem
(a) In the 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?
(b) Generalize this to an grid.
Solution
(a) Let us write the position of any coin as . Then,
. Therefore, there are
different positions for the first coin,
possibilities for the second coin,
possibilities for the third coin, and
possibility for the fourth coin. Together, there are
possible placements of the two coins.
(b)Using the same process above, the possible positions of a coin at , where
, can be counted as
possibilities for the first coin,
possibilities for the second coin,
possibilities for the third coin, and
possibilities for the fourth coin. Finally, there are
possibilities.
See also
2010 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
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 |