gaokao 2024 Q14

gaokao · China · national-II 5 marks Combinations & Selection Distribution of Objects to Positions or Containers
In the $4 \times 4$ grid table shown in the figure, select 4 squares such that each row and each column contains exactly one selected square. The total number of ways to do this is $\_\_\_\_$. Among all selections satisfying the above requirement, the maximum sum of the 4 numbers in the selected squares is $\_\_\_\_$.
11213140
12223342
13223343
15243444
In the $4 \times 4$ grid table shown in the figure, select 4 squares such that each row and each column contains exactly one selected square. The total number of ways to do this is $\_\_\_\_$. Among all selections satisfying the above requirement, the maximum sum of the 4 numbers in the selected squares is $\_\_\_\_$.

\begin{center}
\begin{tabular}{ | l | l | l | l | }
\hline
11 & 21 & 31 & 40 \\
\hline
12 & 22 & 33 & 42 \\
\hline
13 & 22 & 33 & 43 \\
\hline
15 & 24 & 34 & 44 \\
\hline
\end{tabular}
\end{center}