# Random Operations

$\Huge{\color{black}{\boxed{1}}} \ \Huge{\color{red}{\square}} \ \Huge{\color{black}{\boxed{5}}} \ \Huge{\color{red}{\square}} \ \Huge{\color{black}{\boxed{2}}} \ \Huge{\color{red}{\square}} \ \Huge{\color{black}{\boxed{3}}} \ \Huge{\color{red}{\square}} \ \Huge{\color{black}{\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 $$1,2,3,4,5$$ in the black boxes in any order that you want. Which of these orderings gives the maximum expected value for the expression?

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