Number of Arrangements of n Objects of m Types/Examples/10 people in 3 groups sizes 5, 3, 2

Example of Use of Number of Arrangements of $n$ Objects of $m$ Types
Let $N$ be the number of ways $10$ people can be partitioned into $3$ sets: one with $5$, one with $3$ and one with $2$ people.

Then:
 * $N = 2520$

Proof
Here we have an instance of Number of Arrangements of $n$ Objects into $3$ Types, such that:
 * $n = 10$
 * $p = 5$
 * $q = 3$
 * $r = 2$

Hence we have:
 * $N = \dfrac {10!} {5! \, 3! \, 2!} = \dfrac {3628800} {120 \times 6 \times 2} = 2520$

Hence the result.