How many ways are there to distribute k distinct objects int

How many ways are there to distribute k distinct objects into five (distinct) boxes with at least one empty box?

Solution

Here main requirement is n>=k,

So, the formula will be :
[ nC0(n0)^knC1(n1)^k+nC2(n2)^k++(1)^(n1)nC(n1)(1)^k]