How many non-decreasing functions exist which map $\{1, 2, \dots, n\} \to \{1, 2, \dots, m\}$?
i.e
How many ordered pairs $(x_1, x_2, \dots, x_n)$ exist such that
$x_i \le x_{i+1}$ and $ 1 \le x_i \le m$ for all $i$?
[Solution]
i.e
How many ordered pairs $(x_1, x_2, \dots, x_n)$ exist such that
$x_i \le x_{i+1}$ and $ 1 \le x_i \le m$ for all $i$?
[Solution]
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