Final answer:
The question is about set theory concerning three overlapping sets and finding the total number of members in exactly one group. None of the provided options (A, B, C, or D) correctly represent the total members in exactly one group.
Step-by-step explanation:
The student is asking about set theory, specifically about finding the total number of members in exactly one group when considering three overlapping sets.
Option A, n(A ∩ B ∩ C), represents the number of elements that are in all three sets A, B, and C. Option B, n(A ∪ B ∪ C), would give the total number of elements in at least one of the sets A, B, or C, also known as the union of the sets.
Option C, n(A ∩ B) - n(A ∩ B ∩ C), subtracts the number of elements in all three sets from the number of elements in both sets A and B, which does not represent the number of elements in exactly one set.
Finally, Option D, n(U) - n(A ∩ B ∩ C), would give the total number of elements in the universe minus those in all three sets, which is not specified in the question as being the number in exactly one group.
Therefore, none of the provided options precisely indicate the total number of members in exactly one group. To find the number of members in exactly one group, one would need to calculate the total members in each individual set and subtract those that are in two sets and three sets from this total. This can be represented with an inclusion-exclusion principle formula that is beyond the scope of the provided options.