1. Let the set $P=\{1,2,3, \cdots, n\}(n \geqslant 7), P$'s subset $A=\left\{a_{1}, a_{2}, a_{3}\right\}$, where $a_{1}<a_{2}<a_{3}$, when it satisfies $a_{3} \geqslant a_{2}+3 \geqslant a_{1}+6$, we call subset $A$ a "good subset" of $P$, then the number of such good subsets is $\qquad$ .
1. $C_{n-4}^{3}$ Detailed Explanation: Arrange $n$ numbers from left to right in ascending order, then the number of numbers less than or equal to $a_{1}$ is $x_{1}$, the number of numbers greater than $a_{1}$ and less than or equal to $a_{2}$ is denoted as $x_{2}$, the number of numbers less than or equal to $a_{3}$ and greater than $a_{2}$ is denoted as $x_{3}$, and the number of numbers greater than $a_{3}$ is denoted as $x_{4}$. Thus, we have $x_{1}+x_{2}+x_{3}+x_{4}=n\left(x_{1} \geqslant 1, x_{2} \geqslant 3, x_{3} \geqslant 3, x_{4} \geqslant 0\right)$, and let $y_{1}=x_{1}, y_{2}=x_{2}-2, y_{3}=x_{3}-2, y_{4}=x_{4}+1$. Therefore, the original problem is transformed into finding the number of positive integer solutions to the equation $y_{1}+y_{2}+y_{3}+y_{4}=n-3$, and then using the stars and bars method.