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 $2 \times 2$?