Question 30$P$ is the set $\{1,2,3,\ldots,14,15\}$. If $A=\{a_1,a_2,a_3\}$ is a subset of $P$ where $a_1\lt a_2\lt a_3$ such that $a_1+6\le a_2+3\le a_3$, how many such subsets of $P$ are there?