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**1. The problem statement, all variables and given/known data**

Compute ##S(n,3)##.

**2. Relevant equations**

**3. The attempt at a solution**

To compute this I used the fact that ##S(n,2) = 2^{n-1}-1## and used the recurrence relation ##S(n,k) = kS(n-1,k) + S(n-1,k-1)##, and used induction to get that ##S(n,3)=\frac{3^{n-1}+1}{2}-2^{n-1}##.

But is there a quicker way to do this? Is there a way to just see plainly, as in, just counting how many ways we could put ##n## distinguishable balls into ##3## indistinguishable boxes where no box is empty? I tried but it seems difficult.