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A math conference is presenting a lecture series with six different lecturers. If Dr. Smith's lecture depends on Dr. Jones's lecture, so that Dr. Smith must be scheduled at some time after Dr. Jones, in how many orders can the six lecturers be scheduled?

 Mar 20, 2020
 #1
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I think basically, this is saying smith and jones must be next to each other

   there are 5 ways to make that happen in 6 time slots

     the other 4 time slots can be distributed 4! ways      5 x 4!   = 120 ways  

 Mar 21, 2020
edited by ElectricPavlov  Mar 21, 2020
 #2
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There are a total of \(6!\) ways to order the \(6\) lectures with no restriction. By symmetry, exactly half of these will have Dr. Jones's lecture before Dr. Smith's lecture. Thus there are \(\dfrac{6!}{2}=360\) ways to schedule the conference.

 Mar 28, 2020

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