Twelve people join hands for a circle dance. In how manydifferent ways can they do this? part (b) Suppose 6 of these people are men and the other six are womenin how many ways can they join hands for a circle dance, assumingthey alternate in gender around the circle?

Twelve people join hands for a circle dance. In how manydifferent ways can they do this? part (b) Suppose 6 of these people are men and the other six are womenin how many ways can they join hands for a circle dance, assumingthey alternate in gender around the circle?

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asked 2021-03-10
Twelve people join hands for a circle dance. In how manydifferent ways can they do this?
part (b)
Suppose 6 of these people are men and the other six are womenin how many ways can they join hands for a circle dance, assumingthey alternate in gender around the circle?

Answers (1)

2021-03-12

Twelve people join hands for a circle dance. In how manydifferent ways can they do this? \((12-1)!=11!\) ways.
part (b)
Suppose 6 of these people are men and the other six are womenin how many ways can they join hands for a circle dance, assumingthey alternate in gender around the circle?
6 men can be arranged in a circle in \((6-1)! =5!\)ways. Then the 6gaps in the circle can be filled in by the 6 ladies in (6-1)\(!=5!\)ways.
Thus a circular arrangement with men and womenalternating can be made in \(5!\times5!\) ways.

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