Study the following information carefully and answer the question given below

Eight persons from A to H has different degree i.e., BBA, MBA and MCA but not necessarily in the same order. At least two but not more than three persons have the same degree. Consecutive alphabetically named persons do not have the same degree.

D does not have an MBA degree. Only C and F have the same degree but not a BBA degree. Both A and H have the same degree but not as D have. E does not have an MBA degree. B does not have a BBA degree.

Which of the following degrees has the least students?

The correct option is MBA.

Step-by-step Explanation:

Let's systematically arrange the given information to find the degree of each person from A to H.

1. Basic Rules & Constraints:
- Total persons: 8 (A, B, C, D, E, F, G, H)
- Degrees available: BBA, MBA, MCA
- Each degree must have at least 2 and at most 3 persons.
- Consecutive alphabetically named persons (e.g., A and B, B and C, C and D, etc.) CANNOT have the same degree.

2. Analyzing Specific Conditions:
- "Only C and F have the same degree but not a BBA degree."
This means the degree shared by C and F has exactly 2 persons (since "Only C and F" have it).
Since they don't have BBA, their degree is either MBA or MCA.
- "D does not have an MBA degree" and "E does not have an MBA degree."
- "Both A and H have the same degree but not as D have."
- "B does not have a BBA degree."

3. Determining C and F's Degree:
- Suppose C and F have MBA. Since only C and F can have this degree, no one else has MBA. But then D (not MBA), E (not MBA), B (not BBA ⇒ MBA or MCA, but cannot be MBA since only C & F have it, so B must be MCA).
Let's check if C and F are MCA:
If C and F have MCA, then MCA has exactly 2 persons (C and F).
Then the remaining 6 persons must be distributed between BBA and MBA. Since each degree can have at most 3 persons, BBA and MBA must have 3 persons each (3 + 3 + 2 = 8).
Now let's check D and E: D does not have MBA, so D must have BBA. E does not have MBA, so E must have BBA.
Since D and E are consecutive alphabetically, both having BBA would violate the rule that consecutive alphabetically named persons cannot have the same degree! Thus, C and F CANNOT have MCA.

Therefore, C and F MUST have MBA.
Since only C and F have MBA, the number of students having MBA is 2.
Consequently, MBA is the degree with only 2 students (the minimum possible per degree), while the other two degrees (BBA and MCA) will have 3 students each (3 + 3 + 2 = 8 total persons).

4. Complete Distribution Verification:
- Total students with MBA = 2 (C and F)
- Total students with BBA = 3
- Total students with MCA = 3
Since 2 is the smallest count among all three degrees, MBA has the least students.

Hence, the degree that has the least students is MBA.