Question

Find the number of circular 3-permutations of 5 people.

Answer 1

Answer on Question #75727 – Math – Discrete Mathematics

Firstly, there are $\binom{5}{3} = 10$ different ways of choosing three people to sit at the table. Once we pick three people A, B and C to sit at the table. There are

$$\frac{\text{ways to sit three people in a row}}{\text{ways to rotate the table}} = \frac{\text{ways to sit three people in a row}}{\text{number of chairs}} = \frac{3!}{3} = 2,$$

ways to sit 3 people at a circular table. Hence, there are

$$10 \times 2 = 20$$

3-permutations of 5 people.

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