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anonymous

  • one year ago

How many ways can a teacher arrange four students in the front row with a total of 30 students?

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  1. anonymous
    • one year ago
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    I'm confused

  2. anonymous
    • one year ago
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    Is this a combination or a permutation? What do you think?

  3. anonymous
    • one year ago
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    Idk

  4. anonymous
    • one year ago
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    Permutation?

  5. anonymous
    • one year ago
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    Does the order in which the four students placed in the front row matter?

  6. anonymous
    • one year ago
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    Yes?

  7. anonymous
    • one year ago
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    So let's say that Bill, Jim, Sue, and Betty are chosen to sit in the front row. Does it matter in what order they sit?

  8. anonymous
    • one year ago
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    No

  9. anonymous
    • one year ago
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    Great. So, as long as those four are chosen, it doesn't matter in which order they're chosen. If the order doesn't matter, is that a combination or a permutation?

  10. anonymous
    • one year ago
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    Permutation?

  11. anonymous
    • one year ago
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    Sorry, no. If the order doesn't matter, then it's a combination. If the order does matter, then it's a permutation. So this question is about calculating a combination. Do you know how to do that?

  12. anonymous
    • one year ago
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    No

  13. anonymous
    • one year ago
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    The number of combinations of choosing r items out of a set on n items is given by\[_{n}C _{r}=\frac{ n! }{ r!\left( n-r \right)! }\]Do you understand this equation?

  14. anonymous
    • one year ago
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    No

  15. anonymous
    • one year ago
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    OK. In this question, n is the total number of people. How many is that?

  16. anonymous
    • one year ago
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    30

  17. anonymous
    • one year ago
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    Yup. And r is the number of people that are chosen to sit in the front row. How many is that?

  18. anonymous
    • one year ago
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    4

  19. anonymous
    • one year ago
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    Right. So the calculation becomes\[_{30}C _{4}=\frac{ 30! }{ 4!\left( 30-4 \right)! }=\frac{ 30! }{ 4!26! }\] Can you calculate this answer?

  20. anonymous
    • one year ago
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    Not really

  21. anonymous
    • one year ago
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    Do you know what the factorial symbol (!) means?

  22. anonymous
    • one year ago
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    4!x26! ?

  23. anonymous
    • one year ago
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    Yes

  24. anonymous
    • one year ago
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    I'm using a scientific calculator

  25. anonymous
    • one year ago
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    Great. So you have\[_{30}C _{4}=\frac{ 30\times29\times28\times27\times26\times25\times24\times...\times2\times1 }{\left( 4\times3\times2\times1 \right)\left( 26\times25\times24\times...\times2\times1 \right) }\]Make sense?

  26. anonymous
    • one year ago
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    If so, there are a lot of common factors in the numerator and denominator that cancel out.

  27. anonymous
    • one year ago
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    Still there?

  28. anonymous
    • one year ago
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    Yes sorry had to do something

  29. anonymous
    • one year ago
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    Cancel out the common factors and calculate the result. What do you get?

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