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anonymous

  • one year ago

In a certain summer school program, there are five periods in the day. Each student takes English, Math, History, Science, and Science Lab. In how many orders can a student schedule be arranged given that Science lab must immediately follow the Science class?

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  1. DebbieG
    • one year ago
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    Since Lab must always follow Science, you can treat them as "one class" - so you are really ordering 4 classes into 4 slots. Do you know a rule that tells you how to do that?

  2. DebbieG
    • one year ago
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    Have you learned something called the Fundamental Counting Rule?

  3. anonymous
    • one year ago
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    yea it's basically permutations

  4. DebbieG
    • one year ago
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    Right. So it's a permutation of 4 objects.

  5. anonymous
    • one year ago
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    Can you explain to me why it's 4 x 3 x 2 x 1 x 1

  6. anonymous
    • one year ago
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    The 4 i understand because it has to be Science no matter what

  7. anonymous
    • one year ago
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    Having a hard time understanding the two 1's

  8. DebbieG
    • one year ago
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    Right. If you do it as a permutation of 4 from from objects, then it's 4!/0! = 4!/1 = 4! = 4*3*2*1 Is your answer showing 2 1's? I don't really think that's necessary, but here's my guess: You are ordering a series of objects with n1, n2, n3... etc choices for each phase of the series., the fundamental counting rule says that you take the product of the n's, right? So for the first class, you have 4 choices, for the 2nd class, you have 3 choices, then 2, then 1, THEN you have 1 choice for the lab - it always has to go AFTER the science class.

  9. DebbieG
    • one year ago
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    Personally, I think it's a slightly convuluted way of modeling it. I would rather think of the lab + class as ONE item, so you are really ordering just 4 items into 4 time slots. But I guess you could look at it as 5, it's just that the 5th item - the lab - has only 1 choice as to where it can go. lol

  10. anonymous
    • one year ago
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    hmmmm kinda confusing

  11. DebbieG
    • one year ago
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    It would just depend on how your textbook presented this type of problem. I agree, no need for the extra x1, but then, it doesn't change the answer either. :)

  12. anonymous
    • one year ago
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    so if there isnt a extra one then what would be there

  13. DebbieG
    • one year ago
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    I would expect the answer to be 4 x 3 x 2 x 1 If you have an answer key that gives 4 x 3 x 2 x 1 x 1, I'm not sure why the extra 1 is needed. So I'm not sure what you're asking...?

  14. anonymous
    • one year ago
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    nvm thanks

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