Random Operations

1 5 2 3 4 \Huge{\color{#333333}{\boxed{1}}} \ \Huge{\color{#D61F06}{\square}} \ \Huge{\color{#333333}{\boxed{5}}} \ \Huge{\color{#D61F06}{\square}} \ \Huge{\color{#333333}{\boxed{2}}} \ \Huge{\color{#D61F06}{\square}} \ \Huge{\color{#333333}{\boxed{3}}} \ \Huge{\color{#D61F06}{\square}} \ \Huge{\color{#333333}{\boxed{4}}} \

The four red boxes will be filled in with the operators + , +, , -, × , \times, and ÷ \div , randomly and without repetition.

However, you can rearrange the numbers 1 , 2 , 3 , 4 , 5 1,2,3,4,5 in the black boxes in any order that you want. Which of these orderings gives the maximum expected value for the expression?

5 , 4 , 3 , 2 , 1 5,4,3,2,1 5 , 4 , 1 , 2 , 3 5,4,1,2,3 5 , 3 , 1 , 4 , 2 5,3,1,4,2 1 , 2 , 3 , 4 , 5 1,2,3,4,5 5 , 1 , 2 , 3 , 4 5,1,2,3,4

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