Problem:
Six chairs are arranged around a round table. Two students and two teachers randomly select four of the chairs to sit in. What is the probability that the two students will sit in two adjacent chairs and the two teachers will also sit in two adjacent chairs?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If we look around the circle, we can seat the people in total ways (with full distinguishability).
However, if our condition is met, we will first seat the teachers in ways (the second teacher must occupy one of the two adjacent spots).
Then, the remaining students can choose their seats in ways (there are chairs left, so there are pairs of adjacent seats, and orders for them to sit in).
Thus our overall probaility is
which gives us an answer of
The problems on this page are the property of the MAA's American Mathematics Competitions