To determine the number of elements in the sample space using the counting principle, we consider how many choices are available for each selection.

Here, two digits are selected without replacement from the digits 1, 2, 3, and 4.

Step-by-step approach:

1. First selection: We have 4 digits to choose from initially: {1, 2, 3, 4}. Therefore, there are 4 possible choices for the first digit.
2. Second selection: Since we are selecting without replacement, one digit is already chosen. That leaves 3 remaining digits to choose from for the second selection.

By the counting principle, we multiply the number of choices for each selection:

$\text{Total number of elements} = 4 \times 3 = 12$

Conclusion:

There are 12 possible outcomes (elements in the sample space) when two digits are selected without replacement from the set {1, 2, 3, 4}.

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Do you want more details or have any questions about this process?

Here are 5 related questions to explore:

1. How would the result change if digits could be selected with replacement?
2. What are the actual pairs formed in the sample space?
3. How would the sample space change if three digits were selected instead of two?
4. Can you calculate the number of outcomes if the order of selection didn’t matter?
5. How would the problem differ if you selected from digits 1 to 5 instead of 1 to 4?

Tip: When selecting items without replacement, the number of available choices decreases after each selection!