In how many can 7 different objects be divided among 3 persons so that either…
2025
In how many can 7 different objects be divided among 3 persons so that either one or two of them do not get any object?
Answer: C. 381 — Answer: 381 Step 1: Count distributions where exactly one person gets no object. Choose which person gets nothing: 3 ways. For the remaining two people, each…
- A.
375
- B.
378
- C.
381
- D.
385
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Correct answer: C
Answer: 381
Step 1: Count distributions where exactly one person gets no object.
Choose which person gets nothing: 3 ways.
For the remaining two people, each of the 7 distinct objects can go to either person: 2^7 total assignments, but exclude the 2 assignments where all objects go to one person, so valid splits = 2^7 - 2 = 126.
Total for this case: 3 * 126 = 378.
Step 2: Count distributions where exactly two people get no objects.
Exactly one person gets all 7 objects: 3 ways (choose which person).
Total ways = 378 + 3 = 381.