Each of four students hands in a homework paper. later the teacher hands back the graded papers randomly, one to each of the students. in how many ways can the papers be handed back such that every student receives someone else's paper? the order in which the students receive their papers is irrelevant.

9 possible ways.

Step-by-step explanation:

To explain this problem i'm going to use letters and numbers (only as example). The letters correspond to a student and the numbers to a homework. Te correct form we have is:

Student ⇒ Homework

    A       ⇒    1

    B       ⇒    2

    C       ⇒    3

    D       ⇒    4

In how many ways can the papers be handed back such that every student receives someone else's paper?. To answer this we need to form every group of Student/Homework possible, but not taking into count the correct way (showing above)

Possible groups:

1) A-2/B-1/C-4/D-3

2)A-2/B-4/C-1/D-3

3)A-2/B-3/C-4/D-1

4)A-3/B-1/C-4/D-2

5)A-3/B-4/C-2/D-1

6)A-3/B-4/C-1/D-2

7)A-4/B-1/C-2/D-3

8)A-4/B-3/C-2/D-1

9)A-4/B-3/C-1/D-2

We have 9 possible ways,