4 aliens and 4 chairs
Four aliens sit in four chairs, but they don't always sit in the chairs correctly... Sometimes they face forward, and sometimes they face backward.
How many different ways can the four aliens sit in the four chairs?
Clarification : The chairs are in a row and are distinct. The aliens are also distinct (as are their fronts and backs). Each alien can choose a different chair and a different way to face. So for example, the first chair could have a blue alien facing backward or a red alien facing forward.
Image credit: http://drydenart.weebly.com/
The answer is 384.
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1 solution
First off there are 4 ! = 2 4 ways they can choose the order of how they sit.
Once they have sat down, each has 2 ways to sit, so they can sit 2 4 = 1 6 different ways.
2 4 ⋅ 1 6 = 3 8 4