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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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?

Benedict · Accepted Answer

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!×5! ways.

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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