$In how many different ways $n$ persons can seat around a round table?$

Question

$In how many different ways $n$ persons can seat around a round table?$

I am confused about counting all possible ways that $n$ persons can seat around a round table.

Discrete Mathematics Combinatorics Permutation

Mathlearner

28

Report

Answer

The answer is accepted.

Join Matchmaticians Affiliate Marketing Program to earn up to 50% commission on every question your affiliated users ask or answer.

Answer 1

Answers can be viewed only if

The questioner was satisfied and accepted the answer, or
The answer was disputed, but the judge evaluated it as 100% correct.

View the answer

Let the first person seat. Since the table is round, all $n$ options of the first person are similar. Hence the first person can seat in only one different way. After the first person seats the second person has $n-1$ different seats to choose from. The third person would have $n-2$ options and so on. Hence the number of different ways that $n$ persons can seat around a round table is
\[1 \times (n-1) \times (n-2) \times \cdots 2\times 1=(n-1)!.\]

Erdos

4.4K

$In how many different ways $n$ persons can seat around a round table?$

Answer

Related Questions

Search