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Consider the equation $x_1 + x_2 + x_3 + x_4 = 15\text{.}$ How many solutions are there with $2 \le x_i \le 5$ for all $i \in \{1,2,3,4\}\text{?}$

Hint

Instead, count the solutions to $y_1 + y_2 + y_3 + y_4 = 7$ with $0 \le y_i \le 3\text{.}$ Why is this equivalent?