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mathmath333
 one year ago
There are 20 people among whom two are sisters.
Find the number of ways in which we can arrange
them around a circle so that there is exactly one
person between the two sisters?
mathmath333
 one year ago
There are 20 people among whom two are sisters. Find the number of ways in which we can arrange them around a circle so that there is exactly one person between the two sisters?

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.1\(\large \color{black}{\begin{align} & \normalsize \text{ There are 20 people among whom two are sisters. }\hspace{.33em}\\~\\ & \normalsize \text{ Find the number of ways in which we can arrange }\hspace{.33em}\\~\\ & \normalsize \text{ them around a circle so that there is exactly one}\hspace{.33em}\\~\\ & \normalsize \text{ person between the two sisters?}\hspace{.33em}\\~\\ \end{align}}\)

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5Think of 20 slots laid out like this dw:1442808790743:dw I can't fit all 20, but you get the idea

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5the first and third slots are locked up by the 2 sisters dw:1442808843579:dw

jim_thompson5910
 one year ago
Best ResponseYou've already chosen the best response.5we have 202 = 18 slots left with 18 people left to fill them so there are 18*17*16*...*3*2*1 = 18! ways to fill up the rest of the slots now because there are 2 ways for the sisters to sit in the first and third seats, we double that to say 2*18! total ways to arrange the people
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