andreyb90 andreyb90
  • 14-04-2017
  • Mathematics
contestada

Harry, Peter and 7 girls sit in a row. Harry can't sit in an end seat. In how many ways can they be arranged?

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Аноним Аноним
  • 14-04-2017
all possibilities = 9! 
possibilities that harry sits at an end = 8! + 8! 
possibilities that harry doesn't sit at an end = 9! - 8! -8! 

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Sxerks Sxerks
  • 14-04-2017
List of all possibilities, without restrictions (ie Harry can sit in any of the 9 seats): [tex]9![/tex]
List of all possibilities where Harry sits on either end: [tex]2 \cdot 8![/tex]

Hence, list of all possibilities where Harry doesn't sit on either end: [tex]9! - 2 \cdot 8! = 282,240[/tex] ways.
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