Run & Hide

Discrete Mathematics Level 4

There are 4 human friends of the Mystery Inc. (assuming Scooby-Doo is always with Shaggy) running away from a mysterious ghost, and there are 4 available rooms to hide in.

Any of these rooms can contain up to 4 teenagers or none at all.

If the ghost opens one of these 4 rooms in random, what is the probability that he will see no-one hiding in there?

If this probability can be expressed as \(\dfrac{a}{b}\), where \(a\) and \(b\) are coprime positive integers, enter \(a+b\) as your answer.


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