Fischer Zoo

Discrete Mathematics Level 3

Lisa has 8 animal ornaments she wants to arrange on her shelf which has just 8 spots in a row. There are 2 mice, 2 dogs, 2 frogs, 1 giraffe, and 1 elephant. Lisa knows that elephants are afraid of mice, so she wants to arrange the ornaments so that one mouse is somewhere to the left of the elephant and the other mouse is somewhere to the right of the elephant, to trap the elephant between the mice. She also knows that frogs like to jump around, and hence wants the frogs to have an even number of spots between them. How many different ways can Lisa arrange the animals?

Details and assumptions:

  • The ornaments of the same type are indistinguishable.

  • 0 is an even number. So the frogs having 0 spaces between them, i.e. the frogs being adjacent, is also allowed.


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