We are administering a survey and trying to determine how many permutations exist for the combination of question numbers and and responses in order to check our work.
Specifically, we have a set of three survey questions, and four possible responses for each question. The respondent of the survey can select all that apply, so for each question, a maximum of four and a minimum of one response can be selected for each question.
E.g.: Who is the decision-maker for activity A? Self, spouse, other household member. [apply this question for three activities, with the same responses. multiple responses can be selected.]
How many possible combinations of responses could there be across the three questions?
Formulas in excel or R are welcome. Thanks!!
For each individual questions there are four binary options (checked box or blank box), so each question has $2^4 - 1$ possible answers. The $-1$ is the option where all fields are left blank, which you want to excluse.
Then the total number of possible combinations is $(2^4 - 1)^3$.