A Professor decides to hide their hoard money, 100 identical gold coins, in 20 unique locations...

A Professor decides to hide their hoard money, 100 identical gold coins, in 20 unique locations hidden across the city. It is assumed that multiple coins or even none can be stored at each location.

How many ways can he distribute these coins if neither the Mining Lab location nor the Office location can have more than 20 coins (e.g., 25 coins to the Mining Lab and 25 coins to the Office with 50 coins to other locations would not be legal)? It is assumed they cannot trust any of his colleagues with their precious and hard-earned research funds.

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Colby Messinger answered 11 months ago

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