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Hi there! I was working on my homework when I came across two particularly difficult problems. Help would be appreciated!

 

In how many ways can I distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive at least 1 of each type of candy?

In how many ways can I distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive exactly 3 pieces of candy?
 

 May 19, 2020
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I can do this!

 

1) In how many ways can I distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive at least 1 of each type of candy?

 

By stars and bars, the number of ways is c(8,3)*c(8,3) = 3136.

 

2) In how many ways can I distribute 6 identical gummy bears and 6 identical chocolates to 4 students, if each student must receive exactly 3 pieces of candy?

 

By stars and bars, this is c(14,4) = 1001.

 May 19, 2020

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