MathNet 2009-part-01 — 175 problems (EN–VI) Question 138

The set of the permutation $X = (x_1, x_2, \dots, x_9)$ of $1, 2, \dots, 9$ is $A$. $\forall X \in A$, and let $f(X) = x_1 + 2x_2 + 3x_3 + \dots + 9x_9$, $M = \{f(X) \mid X \in A\}$. Find the value of $|M|$. (Posed by Xiong Bin)