The number of arrangements of six identical balls in three identical bins…
2022
The number of arrangements of six identical balls in three identical bins is______.
Attempted by 64 students.
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Correct answer: 7
Answer: 7.
Explanation: Since the bins are identical and may be empty, we need the number of partitions of 6 into at most three parts (order does not matter). List all such partitions:
6
5 + 1
4 + 2
4 + 1 + 1
3 + 3
3 + 2 + 1
2 + 2 + 2
There are 7 such partitions, so the number of arrangements is 7.