Question

a social scientist conducts a study with 10 subjects. in which situations is a permutation necessary to determine the number of possible outcomes?
administer a survey to 6 of the subjects.
select 3 out of 6 sandwiches and 2 out of 4 desserts for the subjects lunches.
schedule interviews for all 10 subjects.
create a seating chart for the 10 subjects around a table.
invite 3 subjects to participate in a repeat study.

Explanation:

Step1: Recall permutation concept

Permutation is used when order matters.

Step2: Analyze "Administer a survey to 6 of the subjects"

Order of selecting 6 subjects for survey doesn't matter, so no permutation.

Step3: Analyze "Select 3 out of 6 sandwiches and 2 out of 4 desserts for the subjects’ lunches"

Order of selecting food items doesn't matter, so no permutation.

Step4: Analyze "Schedule interviews for all 10 subjects"

Order of scheduling interviews matters (e.g., 9 - 10 am is different from 10 - 11 am for a subject), so permutation is needed.

Step5: Analyze "Create a seating chart for the 10 subjects around a table"

Order of seating matters, so permutation is needed.

Step6: Analyze "Invite 3 subjects to participate in a repeat study"

Order of inviting 3 subjects doesn't matter, so no permutation.

Answer:

Schedule interviews for all 10 subjects; Create a seating chart for the 10 subjects around a table