Mathematics Question from JEE Main 2025 · 24 January, Shift 1

Let $S = \{p_1, p_2, \dots, p_{10}\}$ be the set of the first ten prime numbers. Let $A = S \cup P$, where $P$ is the set of all possible products of distinct elements of $S$. Then the number of all ordered pairs $(x, y)$, where $x \in S$, $y \in A$, and $x$ divides $y$, is _____.