SOLUTION: A teacher randomly hands back test papers to 4 students. In how many ways can all 4 students receive someone else's paper? I think the solution uses the following reasoning: 3

Question 853340: A teacher randomly hands back test papers to 4 students. In how many ways can all 4 students receive someone else's paper?
I think the solution uses the following reasoning:
3 possible "wrong" papers each student can receive. 3x3x3x3=81
81 ways all can receive someone else's paper(?)
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
4 items taken 4 at a time gives you 24 possible outcomes
1 2 3 4
1 2 4 3
1 3 2 4
1 3 4 2
1 4 2 3
1 4 3 2
2 1 3 4
2 1 4 3
2 3 1 4
2 3 4 1
2 4 1 3
2 4 3 1
3 1 2 4
3 1 4 2
3 2 1 4
3 2 4 1
3 4 1 2
3 4 2 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
And only one of these permutations is correct.
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