In how many ways can we distribute 16 chocalate donuts, 13 glazed donuts, and 15 jelly donuts among 4 people if each person insists on receiving at least 2 of each variety of donut? Help wanted soon please!
+6248 We can allocate the flavors separately, and take the product of the number of allocations of each flavor.
First off we give everyone their 2 donuts of each flavor.
That leaves 8 chocolate, 5 glazed, and 7 jelly.
Allocating each flavor is equivalent to sorting balls into bins with no restrictions. Thus we have
\(N = \dbinom{8+4-1}{4-1}\dbinom{5+4-1}{4-1}\dbinom{7+4-1}{4-1} = 1108800\)
