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A team has 10 members of different heights. Howmany ways are there forthe members to line up in two rows of five people so that each member in the back row is taller than the one imediately in front?

 Dec 18, 2018

Best Answer 

 #1
avatar+6252 
+2

Split the team up into 2 subteams by heightThe tallest 5 is one subteam, the shortest 5 the otherAny member of the tall team can stand in the backAny member of the short team can stand in frontThere are 5! ways for the 5 tall team members to arrange themselvesThere are also 5! arrangements for the short team membersThus there are 5!×5!=1202=14400 different arrangements

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 Dec 18, 2018
 #1
avatar+6252 
+2
Best Answer

Split the team up into 2 subteams by heightThe tallest 5 is one subteam, the shortest 5 the otherAny member of the tall team can stand in the backAny member of the short team can stand in frontThere are 5! ways for the 5 tall team members to arrange themselvesThere are also 5! arrangements for the short team membersThus there are 5!×5!=1202=14400 different arrangements

Rom Dec 18, 2018

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