Chapter 4 - Probability and Counting Rules - 4-4 Counting Rules - Exercises 4-4 - Page 237: 66

495 and 576

There are 4 classes, so there are 4 presidents, 4 vice presidents, and 4 secretary-treasurers forming a pool 12 for selection. We need 4 officers in the council, it is a combination: 4 out of 12 $_{12}C_4$=495 President: 1 out of 4, same for vice president and secretary, treasurer: 1 out of (12-3=9) The total would be $_4C_1$*$_4C_1$*$_4C_1$*$_{9}C_1$=576