10. Joey has 30 thin sticks, each with a length of an integer from 1 centimeter to 30 centimeters. Joey first places three sticks on the table with lengths of 3 centimeters, 7 centimeters, and 15 centimeters, and then selects a fourth stick to form a convex quadrilateral with the first three sticks. Joey has ( ) different ways to choose the fourth stick.
(A) 16
(B) 17
(C) 18
(D) 19
(E) 20
10. B.

Let the length of the fourth stick be $x$ cm. Then
$$
\left\{\begin{array}{l}
x+3+7>15, \\
3+7+15>x
\end{array} \Rightarrow 5<x<25\right. \text {. }
$$

Also, $x \in \mathbf{Z}$, so $x$ can take 19 different integer values, but 7 and 15 have already been taken, leaving 17 choices.