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?

Guest May 19, 2020

#1**0 **

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.

Guest May 19, 2020