10. Let $a_{1}, a_{2}, a_{3}, a_{4}, a_{5}$ be a permutation of the numbers $1,2,3,4,5$. If there do not exist $1 \leqslant i<j<k \leqslant 5$ such that $a_{i}<a_{j}<a_{k}$, then the number of all such permutations is $\qquad$.