To answer the question of which four volunteers were chosen, let's break down the steps involved in the process that the courtroom clerk used:
1. Identify two-digit numbers from the provided sequence:
The given sequence is:
[tex]\[10631 \ 09728 \ 68702 \ 27963 \ 02477 \ 55494 \ 39563\][/tex]
We read the sequence in two-digit segments, starting from the left:
[tex]\[10 \ \underline{63} \ 10 \ \underline{97} \ 28 \ \dots \][/tex]
Continuing this process, we derive the following two-digit sequences:
[tex]\[10, 63, 10, 97, 28, 68, 70, 22, 79, 63, 02, 47, 77, 55, 49, 43, 95, 63\][/tex]
2. Filter the two-digit numbers:
We need to choose numbers that fall between 01 and 28, and ignore duplicates along the way. We will also ignore any invalid numbers (00, numbers greater than 28) and stop once we have selected four valid unique numbers.
Let's proceed step by step:
- 10: This number is between 01 and 28. We select 10 as our first volunteer.
- 63: This number is greater than 28, so it's ignored.
- 10: This number has already been selected, so it's ignored.
- 97: This number is greater than 28, so it's ignored.
- 28: This number is between 01 and 28. We select 28 as our second volunteer.
- 68: This number is greater than 28, so it's ignored.
- 70: This number is greater than 28, so it's ignored.
- 22: This number is between 01 and 28. We select 22 as our third volunteer.
- 79: This number is greater than 28, so it's ignored.
- 63: This number is greater than 28, so it's ignored.
- 02: This number is between 01 and 28. We select 02 as our fourth volunteer.
At this point, we have our four unique valid numbers.
3. List the chosen volunteers:
The final list of chosen volunteers based on their assigned numbers is:
[tex]\[10, 28, 22, 02\][/tex]
Thus, the volunteers chosen by the courtroom clerk are:
Volunteer [tex]\(10\)[/tex], Volunteer [tex]\(28\)[/tex], Volunteer [tex]\(22\)[/tex], and Volunteer [tex]\(02\)[/tex].
