Two digits are selected with replacement from the digits 1, 2, 3, 4, 5, and 6.How many possibilities are there for the first digit?

1. Break Down the Problem

To determine the possibilities for selecting the first digit from the digits 1, 2, 3, 4, 5, and 6, we need to consider that there are no restrictions on the first digit being any of the available digits.

2. Relevant Concepts

Since the digits can be selected with replacement, for the first digit, we can simply select any of the available digits.

3. Analysis and Detail

1. The available digits are: {1, 2, 3, 4, 5, 6}.
2. There are a total of 6 digits to choose from.
3. Since the selection is with replacement, the choice of the first digit does not depend on subsequent selections.

4. Verify and Summarize

As there are 6 unique digits, each selection of the first digit is independent and can be any of those digits. Thus, there are indeed 6 possibilities for the first digit.

Final Answer

There are 6 possibilities for the first digit.