After all students have left the classroom, a statistics professor notices that four copies of the text were left under desks. at the beginning of the next lecture, the professor distributes the four books in a completely random fashion to each of the four students (1, 2, 3, and 4) who claim to have left books. one possible outcome is that 1 receives 2's book, 2 receives 4's book, 3 receives his or her own book, and 4 receives 1's book. this outcome can be abbreviated as (2, 4, 3, 1).
list the 23 other possible outcomes.
a) { (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 3, 2), (1, 4, 2, 3), (2, 1, 3, 4), (2, 3, 4, 1), (2, 3, 1, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 2, 4), (3, 1, 4, 2), (3, 4, 1, 2), (3, 4, 2, 1), (3, 2, 1, 4), (3, 2, 4, 1), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1) }
b) { (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 3, 2), (1, 4, 2, 3), (1, 3, 2, 4), (2, 1, 3, 4), (2, 4, 3, 1), (2, 3, 4, 1), (2, 3, 1, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 4, 2), (3, 4, 1, 2), (3, 4, 2, 1), (3, 2, 1, 4), (3, 2, 4, 1), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1) }
c) { (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 3, 2), (1, 4, 2, 3), (1, 3, 2, 4), (2, 1, 3, 4), (2, 4, 3, 1), (2, 3, 4, 1), (2, 3, 1, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 2, 4), (3, 1, 4, 2), (3, 4, 1, 2), (3, 4, 2, 1), (3, 2, 1, 4), (3, 2, 4, 1), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1) }
d) { (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 3, 2), (1, 4, 2, 3), (1, 3, 2, 4), (2, 1, 3, 4), (2, 3, 4, 1), (2, 3, 1, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 2, 4), (3, 1, 4, 2), (3, 4, 1, 2), (3, 4, 2, 1), (3, 2, 1, 4), (3, 2, 4, 1), (4, 1, 2, 3), (4, 1, 3, 2), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1) }
e) { (1, 2, 3, 4), (1, 2, 4, 3), (1, 3, 4, 2), (1, 4, 3, 2), (1, 4, 2, 3), (1, 3, 2, 4), (2, 1, 3, 4), (2, 3, 4, 1), (2, 3, 1, 4), (2, 1, 4, 3), (2, 4, 1, 3), (3, 1, 2, 4), (3, 1, 4, 2), (3, 4, 1, 2), (3, 4, 2, 1), (3, 2, 1, 4), (3, 2, 4, 1), (4, 1, 2, 3), (4, 2, 1, 3), (4, 2, 3, 1), (4, 3, 1, 2), (4, 3, 2, 1) }