Distributing Distinct Objects into Distinct Boxes: > 1 per box

COMBIN-RYV51E

For $k \geq n$, there is a bijection between the distributions of $k$ distinct objects into $n$ distinct boxes such that each box gets at least one object and

A

the number of functions from a $k$-element set to an $n$-element set

B

the number of one-to-one functions from a $k$ element set to an $n$-element set

C

the number of onto functions from a $k$ element set to an $n$-element set

D

the number of bijections between a $k$-element set and an $n$-element set