help

You want to distribute your 5 distinguishable balls into 3 indistinguishable boxes. Let $B(5,3)$denote the number of ways in which this can be done into exactly 3 indistinguishable non-empty boxes, and use the recurrence relation $B(n,k)=B(n−1,k−1)+kB(n−1,k)$with $B(n,1)=1$ and $B(n,n)=1$. You seek $B(5,1)+B(5,2)+B(5,3)$.

This has something to do with "Stirling numbers" although I am not too sure on this topic. You might consider searching it up!