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**ThePerfectHacker** 2. Given a positive integer $\displaystyle n$ define a $\displaystyle k$-partition to be a sum of $\displaystyle k$ positive integers which sum to $\displaystyle n$. For example, $\displaystyle n=10$. The following are $\displaystyle 4$-partitions. $\displaystyle 10 = 4+4+2+2$ and $\displaystyle 10 = 2+2+4+4$ and $\displaystyle 10 = 1+1+1+7$. Notice that $\displaystyle 2+2+4+4\mbox{ and }4+4+2+2$ are considered distinct*. Say you a given a specific $\displaystyle n$. And given a specific value of $\displaystyle k$, can you find the total number of $\displaystyle k$-partitions of this integer, with a formula?** Now try to see how many partitions (again not counting order) exist for a given integer $\displaystyle n$ (the answer is really supprising).

Hint: Review your Combinatorics formula for this one.