An equal number of KSU and KU fans leave the stadium after a football game and c
ID: 1296897 • Letter: A
Question
An equal number of KSU and KU fans leave the stadium after a football game and cram
into shuttles to be transported to satellite parking lots. Since the final score was 51-13,
any KU fan that sits next to a Wildcat fan will be incessantly mocked for the duration
of the trip. If there are 40 pairs of seats on each shuttle and the fans are arranged
randomly in the seats, how many fans per shuttle will have hurt feelings when they get
to the parking lot? What is the entropy of ways to arrange fans on two seats that do
not result in anyone getting mocked?
Explanation / Answer
Since the seats are arranged in pairs, the possible seating arrangement is
(1) KSU - KU ;(2) KU - KSU ;(3) KSU - KSU ;(4) KU- KU;
For case (1) and (2), KSU fans mock KU fans
So, if the probability of all 4 of the events is equal and (1)+(2)+(3)+(4) = 1
(1)+(2) = 1/2
Therefore, out of the 40 pair of seats, at 20 seats KSU fans per shuttle will be mockng KU fans.
So, 20 fans per shuttle are being mocked.
(b.) For no one to get mocked, either (3) or (4) should be followed,
So, if there are 80 fans in a shuttle, 40 KSU and 40 KU, the possible number of ways => total ways to arrange fans / 2
Total number of ways to arrange the people = 80!
Total ways to arrange fans for no mocking = 80!/2