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Pattern of Islands

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

The council has decided to build bridges linking the islands Ander, Bresh, Calo, Daple and Ellip.
They want to make sure that
  • there will be two bridges leading from each of the islands Ander, Bresh and Calo, and three leading from Ellip and Daple
  • no pair of islands will be joined by more that one bridge
How many different ways are there to do this?