9) Distribute 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 $\qquad$.

Assign 24 volunteer slots to 3 schools, ensuring 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 $\qquad$.
(9) Method 1: Use the gaps between 4 sticks to represent 3 schools, and use “ * ” to indicate quotas. For example,
$$
|* * * *| * \cdots *|* *|
$$

represents the first, second, and third schools having 4, 18, and 2 quotas, respectively. If each “*” and each “|” is considered a position, and the ends must be “|”, the different allocation methods are equivalent to 2 out of 26 (24 + 2) positions (excluding the ends) being occupied by “|”. The “allocation method where each school has at least one quota” is equivalent to choosing 2 gaps from the 23 gaps between 24 “*” to insert “|”, hence there are $C_{23}^{2}=253$ (ways). In the “allocation method where each school has at least one quota,” the number of allocation methods where “at least two schools have the same number of quotas” is 31.
In summary, the number of allocation methods that meet the conditions is $253-31=222$ (ways).
Method 2: Let the number of quotas allocated to the 3 schools be $x_{1}, x_{2}, x_{3}$, respectively. The number of allocation methods where each school has at least one quota is the number of positive integer solutions to the equation $x_{1}+x_{2}+x_{3}=24$, which is equivalent to the number of non-negative integer solutions to the equation $x_{1}+x_{2}+x_{3}=21$. This is equal to the number of combinations with repetition of 21 elements taken from 3 different elements: $\mathrm{H}_{3}^{21}=\mathrm{C}_{23}^{21}=\mathrm{C}_{23}^{2}=253$. In the “allocation method where each school has at least one quota,” the number of allocation methods where “at least two schools have the same number of quotas” is 31.
In summary, the number of allocation methods that meet the conditions is $253-31=222$ (ways).