In the expression 5 * 4 * 3 * 2 * 1, * is chosen from +, -, × each at most two times. What is the smallest non-negative value of the expression?

• The expression is 5 * 4 * 3 * 2 * 1, where the four operators are chosen from {+, -, ×}, with each operator used at most two times.

• To find the smallest non-negative value, we aim for 0, which requires the expression to be a difference of two equal terms or a product involving zero (impossible here as all numbers are non-zero).

• Consider the combination: 5 - 4 - 3 + 2 + 1. Here, '-' is used twice, '+' is used twice, and '×' is used zero times. This satisfies the constraint that each operator is used at most two times.

• Calculating this expression: 5 - 4 = 1; 1 - 3 = -2; -2 + 2 = 0; 0 + 1 = 1. This yields 1, not 0.

• Consider another combination: 5 - 4 - 3 + 2 × 1. Here, '-' is used twice, '+' is used once, '×' is used once. This satisfies the constraints.

• Calculating this expression: 5 - 4 = 1; 1 - 3 = -2; 2 × 1 = 2; -2 + 2 = 0. This yields 0, which is the smallest non-negative value.