SOLUTION: Four women are sitting in chairs. In how many ways can they get up and reseat themselves in such a way that no one is sitting in the chair that she occupied before?

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Question 1143364: Four women are sitting in chairs. In how many ways can they get up and reseat themselves in such a way that no one is sitting in the chair that she occupied before?
Found 2 solutions by Edwin McCravy, greenestamps:
Answer by Edwin McCravy(20064) About Me  (Show Source):
You can put this solution on YOUR website!
Four women are sitting in chairs. In how many ways can they get up and reseat
themselves in such a way that no one is sitting in the chair that she occupied
before?
It's 4 sub-factorial = !4 = 

   ABCD   <-- their original seating. They can all 4 re-seat in different chairs 9 ways:
1. BADC
2. BCDA
3. BDAC
4. CADB
5. CDAB
6. CDBA
7. DABC
8. DCAB
9. DCBA

Edwin

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


An arrangement of objects in which none of the objects is in the correct place is called a derangement. There is a nice formula for calculating the number of derangements of n objects. For 4 objects, the formula is



For another example -- to show the pattern in the formula -- the formula for the number of derangements of 5 objects is