There are 500 places in a certain theatre, but only 490 : PS Archive
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# There are 500 places in a certain theatre, but only 490

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SVP
Joined: 03 Feb 2003
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There are 500 places in a certain theatre, but only 490 [#permalink]

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13 Oct 2003, 03:01
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There are 500 places in a certain theatre, but only 490 people attend it. What is the probability of their sitting such that the right 10 places in the first row are not occupied?
Intern
Joined: 16 Sep 2003
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Location: Buffalo (NY)
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13 Oct 2003, 05:07
it's kind of tricky...
I did get an answer, but not too sure about it ....

My anser is 1/50^10
SVP
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13 Oct 2003, 05:40
Yes, it is tricky, so I employ a classic formula: P=F/T

T=500C10
F=10C10

I do not have an official answer, so my approach is open for discussion.
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Joined: 30 Oct 2003
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01 Jan 2004, 13:19
490 people can sit in 500 places in 500C490 ways
out of 490 we can choose 10 people in 490C10 ways. These people
occupy 10 seats in 10! ways
Probability that those 10 setas are occupied =
so P = 10! * 490C10 / 500 C 490

Probablity that those 10 seats are empty = 1 - P
01 Jan 2004, 13:19
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# There are 500 places in a certain theatre, but only 490

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