$$3 \text { Shelf empty: }(8,0,0,0) \rightarrow 1 \text { way }$$

$$\left.2 \text { shelf empty: } \begin{array}{c} (7,1,0,0) \\ (6,2,0,0) \\ (5,3,0,0) \\ (4,4,0,0) \end{array}\right] \rightarrow 4 \text { ways }$$

$$\left.1 \text { shelf empty: } \begin{array}{cc} (6,1,1,0) & (3,3,2,0) \\ (4,2,1,0) & (4,2,2,0) \\ (4,3,0) & \end{array}\right] \rightarrow 5 \text { ways }$$

$$\left.0 \text { Shelf empty : } \begin{array}{ll} (1,2,3,2) & (5,1,1,1) \\ (2,2,2,2) \\ (3,3,2,1,1) \\ (4,2,1,1) & \end{array}\right] \rightarrow 5 \text { ways }$$

Total $$=15$$ ways