$\left| {\begin{array}{*{20}{c}}
  L&O&Y \\ 
  2&2&4 \\ 
  { \geqslant 1}&{ \geqslant 1}&{2 \leqslant } 
\end{array}} \right| \Rightarrow \left| {\begin{array}{*{20}{c}}
  L&O&Y \\ 
  1&1&2 \\ 
  1&2&1 \\ 
  2&1&1 \\ 
  2&2&0 
\end{array}} \right|$

Required number of ways

${ = ^2}{C_1}{ \times ^2}{C_1}{ \times ^2}{C_2}{ + ^2}{C_1}{ \times ^2}{C_2}{ \times ^4}{C_1}$ ${ + ^2}{C_2}{ \times ^2}{C_1}{ \times ^4}{C_1}{ + ^2}{C_2}{ \times ^2}{C_2}{ \times ^4}{C_0}$

$ = 2 \times 2 \times \frac{{4 \times 3}}{2}$ $ + 2 \times 1 \times 4 + 1 \times 2 \times 4 + 1 \times 1 \times 1$

$ = 24 + 8 + 8 + 1 = 41$