Problem:
Angie, Bridget, Carlos, and Diego are seated at random around a square table, one person to a side. What is the probability that Angie and Carlos are seated opposite each other?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Proceeding clockwise from Angie, the seating could be: , , or . In of these possibilities Carlos is opposite Angie, so the probability is .
If Angie sits down first, there are three equally likely places for Carlos to sit. Only one of these is opposite Angie. Thus the probability is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions