Under the rules of the "Sea battle" game (no two ships may have a common point), can the following sets of rectangular ships be arranged on a $ 10 \times 10$ square board: $ (a)$ two ships $ 1 \times 4$, $ 4$ ships $ 1 \times 3$, $ 6$ ships $ 1 \times 2$, and $ 8$ ships $ 1 \times 1$; $ (b)$ two ships $ 1 \times 4$, $ 4$ ships $ 1 \times 3$, $ 6$ ships $ 1 \times 2$, $ 6$ ships $ 1 \times 1$, and $ 1$ ship $ 2 \times 2$; $ (c)$ two ships $ 1 \times 4$, $ 4$ ships $ 1 \times 3$, $ 6$ ships $ 1 \times 2$, $ 4$ ships $ 1 \times 1$, and $ 2$ ships $ 2 \times 2$?