The counting principle states that if one event can occur in $m$ ways and a second event can occur in $n$ ways, then the two events together can occur in $m \times n$ ways.

In this problem:

• You are selecting two digits.
• Each digit is selected from the set $\{1, 2, 3, 4, 5, 6\}$.
• Since the digits are selected with replacement, each selection is independent, meaning that for both selections, there are 6 possible choices.

Using the counting principle:

• The first digit can be selected in 6 ways.
• The second digit can also be selected in 6 ways.

Thus, the total number of elements in the sample space is:

$6 \times 6 = 36$

So, there are 36 elements in the sample space.

Would you like any more details or have any questions?

Here are five related questions to further explore:

1. What happens to the number of elements in the sample space if selection is without replacement?
2. How many elements are in the sample space if three digits are selected with replacement?
3. What is the probability of selecting the same digit twice from this set?
4. How does the counting principle change for selecting digits from a different set, such as $\{1, 2, 3, \dots, 9\}$?
5. What is the number of elements in the sample space if we select two digits from $\{1, 2, 3, 4, 5, 6\}$ without replacement?

Tip: In problems involving "with replacement," each selection is independent, meaning each choice has the same number of outcomes.