Re: Another theatre line problem
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10 people stand in a single file line in front of a ticket window. The 10 people have 10 different heights. The ticket clerk can see a person if and only if no one taller stands in front of that person. How many people can the ticket clerk see on average?
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There are 10! ways they can line up.
First arrange them in order 1,2...,9,10 to see all 10. One way to do this.
Number of ways to see exactly 9:
Choose any of the first 9 and move him back one or more places. So, 9+8+7+6+5+4+3+2+1 = 9(9+1)/2 = 45
Number of ways to see exactly 8:
Choose any two of the first 9 and move them back one or more places.
Yikes. There's got to be an easier way.
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