2002 Math OSP, Number 20

Discrete Mathematics Level pending

A marathon competition is followed by four High Schools : Merak, Merpati, Pipit, and Walet. Each High School sends 5 runners. The runners who placed 1st, 2nd, 3rd, 4th, 5th, 6th will earn the points of consecutively: 7, 5, 4, 3, 2, 1. The points of each High School is the total of their 5 runners. The High School with the highest points is the winner. At the end, it was Pipit High School that was the winner and there are no two runners that finish at the same time. How many possibilities are there for the winning High School?

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