Combination or Permutation

Question

A hospital conducts a survey of patients' satisfaction with its service. Each survey respondent ranks the 3 items with which he/she is most satisfied with the hospital service. The items to be ranked include: ease of appointment, courtesy of staff, length of waiting time, hours of operation, friendliness of doctors, thoroughness of examination, and hospital environment. In how many ways can a respondent answer this questionnaire?

Answer 1

Since order (ranking) makes a difference, this problem is a Permutation.

Seven categories are given and they are taken three at a time.

 

₇P₃ = 7! / (7 - 3)!