MATH 475 Final: MATH475 BOYLE-M SPRING2005 0101 FINAL SOL 1

• School: University of Maryland
• Department: Mathematics
• Course: MATH 475
• Professor: All

Document Summary

Math 475 spring 2005 final exam. Solutions (in-class part: fourteen players will be assigned to play poker at three tables: ve at two tables and four at one table. Two assignments of players will be considered the same if each player has the same person sitting to the left. There are 14! ways to place the players in the fourteen seats. Suppose tables a,b,c will have 5,5,4 players: among the 14! seatings, each equivalent seating at a occurs 5 times, each equivalent seating at b occurs 5 times, and each equivalent seating at c occurs 4 times. Finally, interchanging a and b gives us an assignment we regard as the same. Again suppose tables a,b,c will have 5,5,4 players. The number of ways to assign players to tables a,b,c is (14)!/(5!5!4!). The number of arrangements at the tables is 4!4!3! (because the number of ways to circularly order k items is (k 1)!).