HW1-solutions - HW1 Solutions Problem 1: Each of ten people...

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Unformatted text preview: HW1 Solutions Problem 1: Each of ten people simultaneously requests a distinct movie from a new service that broadcasts 3D movies. These 3D movies are broadcast as a left and a right stream, which are distinct. (So 10 distinct movies, 20 distinct streams in total.) But the service is not very reliable, and the 3D effect only works if you receive a matching left and right stream. Assume that each person receives exactly two of the streams, and each stream goes to exactly one person. (a) How many ways are there for the streams to be broadcast if the service provider makes no guarantees about which streams each person receives? (b) How many ways if each person receives a matching left and right stream? (Not necessarily for the movie they ordered.) Assume that movie players are smart enough to sort out which stream is left and which is right, so any matching pair will play properly. (c) How many ways if each person is guaranteed one left stream and one right stream? (Not necessarily for the same movie.) Solution: My intended solutions were as follows. For part (a), there are 20! ways for the streams to be broadcast if there are no guarantees about who gets which streams. For part (b), there are 10! ways to assign the matching pairs to the users, and since the movie players can sort out which is left and which is right, for any of the 10! assignments there are 2 10 ways that the matching pairs can arrive (i.e. (left,right) or (right,left)); thus 10!2 10 . For part (c), there are 10! ways to assign the left streams to users, and likewise 10! ways to assignare 10!...
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HW1-solutions - HW1 Solutions Problem 1: Each of ten people...

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