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An eccentric Computing Science Professor decides to hide their hoard of NSERC funded money, 100 identical...

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Advance Math

An eccentric Computing Science Professor decides to hide theirhoard of NSERC funded money, 100 identical gold coins, in 20 uniquelocations hidden across campus. It is assumed that multiple coinsor even none can be stored at each location.
a) How many ways can they distribute these coins without anyrestrictions?
b) How many ways can they distribute these coins if each locationgets at least 5 coins?
c) How many ways can they distribute these coins if each locationonly gets an even number of coins?
d) How many ways can they distribute these coins if theSessional Instructor Lab location can't have more than 20 coinsdistributed to it?
BONUS: e) How many ways can he distribute these coins if neitherthe Data-Mining Lab location nor the Sessional Instructor officelocation can have more than 20 coins (e.g., 25 coins to theData-Mining Lab and 25 coins to the Sessional Instructor 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.

ONLY ANSWER d) and BONUS.

Please make sure everything is clear and understandable, if it'sgood I will give thumbs up 100%! Thanks.

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