If $$n$$ is the number of ways five different employees can sit into four indistinguishable offices where any office may have any number of persons including zero, then $$n$$ is equal to:

This is the problem of partitioning a set of 5 distinct elements into $$1, 2, 3,$$ or $$4$$ non-empty subsets (since offices are indistinguishable, we use Stirling numbers of the second kind, $$S(n, k)$$).

• 1 office used: $$S(5,1) = 1$$

• 2 offices used: $$S(5,2) = \frac{2^5 - 2}{2} = 15$$

• 3 offices used: $$S(5,3) = 25$$

• 4 offices used: $$S(5,4) = 10$$

Total ways $$n = 1 + 15 + 25 + 10 = \mathbf{51}$$.