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The Coventry School's European debate club has 6 German delegates, 5 French delegates, and 3 Italian delegates. In how many ways can these 14 delegates sit in a row of 14 chairs, if each country's delegates insist on all sitting next to each other?

matth99  Aug 29, 2018
 #1
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tHe AnSwEr Is SiX

ThE aNsWeR iS sIx

Guest Aug 29, 2018
 #2
avatar+90969 
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The Germans can be seated in 6! ways

The French can be seated in 5! ways

And the Italians can be seated in 3! ways

 

And...the groups themselves can  be  ordered in 3! ways on the 14 chairs

 

So....the total arrangements are   6! * 5! * 3! * 3!  =    720 * 120 * 6 * 6   =  3,110,400  arrangements

 

 

 

cool cool cool

CPhill  Aug 29, 2018

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