Circular Permutation Calculator
How many ways can 7 people sit around a round table?
7 distinct items around a circle can be arranged in 720 ways.
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Each answer page uses the same values in the question, result, worked steps, and calculator link so the result is easy to verify.
Circular Permutation Calculator
7 distinct items around a circle can be arranged in 720 ways.
Open answer pageCircular Permutation Calculator
8 distinct items around a circle can be arranged in 5,040 ways.
Open answer pageBinomial Coefficient Calculator
The binomial coefficient C(12, 5) is 792.
Open answer pageCombination Calculator
12 choose 2 without repeats is 66.
Open answer pageCombination With Repetition Calculator
5 choose 3 with repeats allowed is 35.
Open answer pagePermutation With Repetition Calculator
6 choices for 4 ordered positions gives 1,296.
Open answer pageMultiset Permutation Calculator
For item-group counts 3, 2, 1, the number of distinct arrangements is 60.
Open answer pageMultiset Permutation Calculator
For item-group counts 2, 2, 1, 1, 1, the number of distinct arrangements is 1,260.
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