Seven members of a book club sit around a round table. Two seatings count as the same if one can be turned into the other by everyone moving the same number of places around the table. How many different seatings are possible?

120Correct answerYour answer360Correct answerYour answer720Correct answerYour answer5,040Correct answerYour answer

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CorrectNot quiteAnswer C

Correct answer: C

In a row, 7 people can sit in $7! = 5040$ ways.
Around a table, each seating appears 7 times in that count (once for each rotation).
Seatings $= \frac{5040}{7} = 6! = 720$ .

Worth noting

5040 treats the table as a row. 360 also divides by 2 for mirror images, which applies to a necklace, not to people who can tell left from right.

Ten questions from Counting and Basic Probability, at your own pace.

Explanation