10. From the set $\mid 1,2, \cdots, 20$ \}, select 5 numbers”, such that the difference between any two numbers is not less than 4, then there are a total of different ways to select.
10.56

Let $1 \leqslant a_{1}<a_{2}<\cdots<a_{5} \leqslant 20$, and let $b_{i}=a_{i}-3(i-1)$. Then $b_{i+1}-b_{i} \geqslant 1$ and $1 \leqslant b_{1}<b_{2}<\cdots b_{5} \leqslant 8$, so $n=C_{8}^{5}=56$.