The number of arrangements of six identical balls in three identical bins is ___

Answer: 7Concept -- Partitions of an Integer (from Discrete Mathematics by Rosen):Since both balls and bins are identical, we need the number of integer partitions of 6 into at most 3 parts (where each part can be 0 or more, representing the number of balls in each bin).The partitions of 6 into at most 3 non-negative parts (written in non-increasing order): (6,0,0), (5,1,0), (4,2,0), (4,1,1), (3,3,0), (3,2,1), (2,2,2). That gives 7 distinct arrangements.Each partition represents a unique way to distribute 6 identical balls into 3 identical bins, since we don't distinguish between bins or between balls. Total = 7.

GATE-CS is a competitive examination conducted in India. This question is from the 2022 GATE-CS Discrete Mathematics paper.

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This GATE-CS 2022 Discrete Mathematics question has a medium difficulty level and is marked as an important question.

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The number of arrangements of six identical balls in three identical bins is ___

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The number of arrangements of six identical balls in three identical bins is ___

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More Questions from Combinatorics: Counting and Permutations

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