A social scientist conducts a study with 10 subjects. In which situations is a permutation necessary to determine the number of possible outcomes?
Select all that apply.
A. Create a seating chart for the 10 subjects around a table.
B. Invite 3 subjects to participate in a repeat study.
C. Schedule interviews for all 10 subjects.
D. Select 3 out of 6 sandwiches and 2 out of 4 desserts for the subjects' lunches.
E. Administer a survey to 6 of the subjects.
Help please
Im guessing A but not sure what else
To determine when a permutation is necessary, we need to consider situations where the order or arrangement of the elements matters. Let's go through each situation one by one:
A. Create a seating chart for the 10 subjects around a table.
In this situation, a permutation is indeed necessary. The order in which the subjects are seated around the table matters, so we need to use a permutation to determine the number of possible outcomes. Therefore, option A is correct.
B. Invite 3 subjects to participate in a repeat study.
In this situation, a permutation is not necessary because the order in which the subjects are invited does not matter. We are only concerned with selecting 3 subjects out of the total, not their specific arrangement. Therefore, option B is incorrect.
C. Schedule interviews for all 10 subjects.
In this situation, a permutation is also not necessary because the order in which the interviews are scheduled does not matter. We are only concerned with assigning interview times to each subject, not their specific arrangement. Therefore, option C is incorrect.
D. Select 3 out of 6 sandwiches and 2 out of 4 desserts for the subjects' lunches.
In this situation, a permutation is not necessary because the order in which the sandwiches and desserts are selected does not matter. We are only concerned with the total count of sandwiches and desserts, not their specific arrangement. Therefore, option D is incorrect.
E. Administer a survey to 6 of the subjects.
In this situation, a permutation is not necessary because the order in which the subjects receive the survey does not matter. We are only concerned with selecting 6 subjects out of the total, not their specific arrangement. Therefore, option E is incorrect.
In conclusion, the only situation where a permutation is necessary is option A: creating a seating chart for the 10 subjects around a table.