A Professor decides to hide their hoard money, 100 identicalgold coins, in 20 unique locations hidden across the city. It isassumed that multiple coins or even none can be stored at eachlocation.
How many ways can he distribute these coins if neither theMining Lab location nor the Office location can have more than 20coins (e.g., 25 coins to the Mining Lab and 25 coins to the Officewith 50 coins to other locations would not be legal)? It is assumedthey cannot trust any of his colleagues with their precious andhard-earned research funds.
