Question

In a mental health clinic, there are 12 patients. A therapist invites all these patients to join her for group therapy. How many possible groups could she get?

a) 1,024
b) 4,096
c) 4096
d) 8,311

Answer 1

The number of possible groups that the therapist could form with 12 patients is calculated using the power set formula 2n, yielding 4,096 possible groups. The correct answer is b) 4,096 which is also represented by option c).

Step-by-step explanation:

The question asks how many possible groups a therapist could form with 12 patients in a mental health clinic. This is a combinatorics problem, which involves calculating the number of ways to choose members for group therapy. Using the formula for the power set, where the number of possible groups is 2n, with n being the number of patients, we can calculate the number of groups. Here, n is 12, so the number of possible groups is 212 = 4,096. Therefore, the correct answer is b) 4,096, which corresponds to option c as well since both present the same numerical value.