If someone have 4 red bricks and 8 blue bricks and arranges them randomly in a circle,
what is the probability that two red bricks are not side by side?
There are possible arrangements.
(This includes duplication from rotations.)
Place the 8 blue bricks in a circle, leaving a space between them.
Select 4 of the 8 spaces and insert the red bricks.
There are: ways.