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 correct option is 0.

To find the smallest non-negative value of the expression, we need to replace the four asterisks (*) in the expression:
$$5*4*3*2*1$$
using the operators +, -, and × such that each operator is used at most two times.

Let us choose the following operators for the placeholders:
1. First * = -
2. Second * = -
3. Third * = +
4. Fourth * = ×

This gives us the expression:
$$5-4-3+2\times 1$$

First, we verify the frequency constraint for each operator:
- The subtraction operator (-) is used 2 times.
- The addition operator (+) is used 1 time.
- The multiplication operator (×) is used 1 time.
Since every operator is used at most two times, this combination is valid.

Now, we evaluate the expression step-by-step following the standard order of operations (multiplication before addition and subtraction):

Step 1: Perform the multiplication:
$$2\times 1=2$$
Substituting this back, the expression becomes:
$$5-4-3+2$$

Step 2: Perform addition and subtraction from left to right:
- First operation:
$$5-4=1$$
- Second operation:
$$1-3=-2$$
- Third operation:
$$-2+2=0$$

Since 0 is the smallest possible non-negative number, the smallest non-negative value we can obtain is indeed 0.