Question

An eccentric Computing Science Professor decides to hide their hoard of NSERC funded money, 100 identical gold coins, in 20 unique locations hidden across campus. It is assumed that multiple coins or even none can be stored at each location.
a) How many ways can they distribute these coins without any restrictions?
b) How many ways can they distribute these coins if each location gets at least 5 coins?
c) How many ways can they distribute these coins if each location only gets an even number of coins?
d) How many ways can they distribute these coins if the Sessional Instructor Lab location can't have more than 20 coins distributed to it?
BONUS: e) How many ways can he distribute these coins if neither the Data-Mining Lab location nor the Sessional Instructor office location can have more than 20 coins (e.g., 25 coins to the Data-Mining Lab and 25 coins to the Sessional Instructor 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.

ONLY ANSWER d) and BONUS.

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Answer 1