10. Allocate 24 volunteer slots to 3 schools, such that each school gets at least one slot and the number of slots each school receives is different. The number of ways to do this is $\qquad$.
(2008 National High School Competition Problem)
10. The number of ways to allocate at least one quota to each school is equal to the number of positive integer solutions to the indeterminate equation $x_{1}+x_{2}+x_{3}=24$, which is $C_{23}^{2}=$ 253. However, the number of allocation methods where at least two schools have the same number of quotas is 31. Therefore, the number of allocation methods that meet the conditions is $253-31=$ 222.