Problem:
Abby, Bridget, and four of their classmates will be seated in two rows of three for a group picture, as shown.
If the seating positions are assigned randomly, what is the probability that Abby and Bridget are adjacent to each other in the same row or the same column?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
There are possible positions for Abby, and this leaves possible positions for Bridget. Because their order doesn't matter, the two girls can be placed in any of pairs of positions. There are pairs of positions that are adjacent in the top row, pairs that are adjacent in the bottom row, and pairs that are adjacent in the same column. So the probability that they occupy adjacent positions is = .
There is a chance Abby is assigned to a corner position and a chance that Abby is assigned to a middle position. If Abby is assigned to a corner position, there is a chance that Bridget is adjacent to Abby. If Abby is assigned to a middle position, there is a chance that Bridget is adjacent to Abby. Thus, the probability that Abby and Bridget are adjacent to each other in the same row or column is + = .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions