I have some combination questions: (a) The Mathematics departmental office has the following stock of dry-erase markers: 7 Red, 4 Navy blue, 6 Green, 8 Black. They are to be distributed, 1 apiece, to the 25 members of the department. How many outcomes are possible? (b) The Chemistry departmental office has 800 black dry-erase markers. The 25 members of the department may take as many as they like. If 46 markers are taken the ﬁrst day, how many different distributions to the faculty members are possible?

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(c) Repeat (b) with the added stipulation that each faculty member took at least one marker. (d) The Physics departmental oﬃce has the following stock of dry-erase markers: 400 Red, 200 Green, 200 Black. The 25 members of the department may take as many as they like. If 46 Red, 3 Green, and 27 Black markers are taken the ﬁrst day, how many diﬀerent distributions to the faculty members are possible?

for a) I found C(25,8)*C(17,7)*C(10,6)*C(4,4)

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