# $n$ identical oranges to $k$ identical kids [duplicate]

I think that this is quite basic, but I can't seem to get it:

Given $n>0$ identical oranges, and $k \leq n$ identical kids. In how many ways can I divide the oranges between the kids, when every kid gets at least one orange.

Notice that the kids are also identical! I.e it's not two different cases when we switch the amount of oranges between 2 kids.

Thanks!

## marked as duplicate by Gerry Myerson, joriki, Brian M. Scott, Zev ChonolesJan 20 '12 at 16:13

• @168335 I'm not sure I understand what you mean by replaced.. There are $n$ oranges. after you decide to give $m$ to one of the kids, there are $n-m$ left. I hope that's answers your question – IBS Dec 21 '11 at 16:35
Define a partition of the integer $k$ into $n$ parts is a multiset of $n$ positive integers that add to $k$. We use $P(k; n)$ to denote the number of partitions of $k$ into $n$ parts. Thus $P(k; n)$ is the number of ways to distribute $k$ identical objects to $n$ identical recipients so that each gets at least one.
Please note that this $P(k; n)$ has no explicit formula. Also, this is exactly opposite to the notation. So, in your notation, it will be $P(n; k)$, the partition of $n$ oranges to $k$ kids.