Problem:
A set of 25 square blocks is arranged into a square. How many different combinations of blocks can be selected from that set so that no two are in the same row or column?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
After one of the blocks is chosen, of the remaining blocks do not share its row or column. After the second block is chosen, of the remaining blocks do not share a row or column with either of the first two. Because the three blocks can be chosen in any order, the number of different combinations is
The problems on this page are the property of the MAA's American Mathematics Competitions