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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!

 Aug 3, 2019
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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

 

\(N = \dbinom{8+4-1}{4-1}\dbinom{5+4-1}{4-1}\dbinom{7+4-1}{4-1} = 1108800\)

 Aug 3, 2019
edited by Rom  Aug 3, 2019
edited by Rom  Aug 3, 2019

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