How many integer solutions are there to the inequality $y_1 + y_2 + y_3 + y_4 < 184$

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$y_1 + y_2 + y_3 + y_4 < 184$
$y_1>0$

$0< y_2\leq10$

$0\leq y_3\leq17$

$0\leq y_4<19$

Don't really know what to do with the inequality. Can I simply change it to $y_1 + y_2 + y_3 + y_4 + y_5 = 183$? If so, will $y_5\geq 0$?

Edit: So this is what I got, it may or may not be correct: $y_1 + y_2 + y_3 + y_4 + y_5 = 181$ $y_1\geq0, 0\leq y_2\leq9, 0\leq y_3\leq17, 0\leq y_4<19$

(181+4)C4 - (181+4-10)C4 - (181+4-18)C4 - (181+4-19)C4 + (181-19-18-10+4)C4