SOLUTION: (a) Find the number of ways that Magnus can give out 12 identical stickers to 12 of his friends. (Not everyone has to get a sticker.) (b) Find the number of ways that Magnus can

                 Part (a)



In this problem, stickers are not distinguishable, but the friends are.

This problem is equivalent to the question: how many solutions does this equation have

     +  +  + . . . +  = n

in integer non-negative numbers at n= 12, k= 12 ?


The answer is: the number of such solutions is  =  =  = 1352078.


This formula is deduced using so called "stars and bars method".


On "stars and bars method", see this Wikipedia article 

https://en.wikipedia.org/wiki/Stars_and_bars_%28combinatorics%29

or read from my lesson

    - Stars and bars method for Combinatorics problems 

in this site.



                 Part (b)



This problem means that each friend gets exactly one sticker.


And since the stickers are undistinguishable, it means that there is only one scenario 
to distribute stickers in a way, as it is assigned by the problem.