Four teachers decide to swap desks at work. How many ways can this be done if no teacher sits at their previous desk?
Mathematics Specialist Units 1&2 Cambridge
I like this question as it seems easy until you start thinking about it. I think the best approach is a tree diagram.
If we think of the four teachers as A, B, C and D. Then A can no longer sit in A, so the options are B, C and D for the first desk.
For the second desk, If B is in the first desk, then A, C or D could be in the second. If C is in the first desk, then A or D could be in the second (B can’t be in the same desk). If D is in the first desk, then A or C can be in the second desk.
And so on, leaving 9 possibilities
BADC
BCDA
BDAC
CADB
CDAB
CDBA
DABC
DCAB
DCBA