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Why is nPr called [. . .]?

  1. Apr 29, 2015 #1

    s3a

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    I'm just curious, why is nPr called the "number of permutations of n different objects taken r at a time"?
     
  2. jcsd
  3. Apr 29, 2015 #2

    phinds

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    Well, because that's what it IS. What would you like to call it?
     
  4. Apr 29, 2015 #3

    s3a

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    I meant that I don't understand what, in general, is being taken r at a time.
     
  5. Apr 29, 2015 #4

    SteamKing

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    A set of r objects from a group of n total objects.

    It could be playing cards, toppings you put on a pizza, whatever.
     
  6. Apr 29, 2015 #5

    phinds

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    Whatever it is that you are taking the permutations of.
     
  7. Apr 29, 2015 #6

    s3a

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    To be more specific, what is meant by "at a time"?

    For example, the answer to the question "In how many ways can 5 differently coloured marbles be arranged in a row?" is nPn.

    So let's visually illustrate this row of 5 marbles as follows.: _ _ _ _ _

    In this case nPn = 5P5, which is read as the "number of permutations of 5 different objects taken 5 at a time". I get that there are 5 different objects, but I don't get what is being taken 5 at a time; each column will only have 1 marble, not 5.

    P.S.
    This may not have been the best example due to the fact that n = r, but I hope the point still came across.
     
  8. Apr 29, 2015 #7

    phinds

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    Suppose you want 5 marbles taken 3 at a time. The marbles are red, black, white, green, yellow.

    You can do
    red, black, yellow
    red, yellow, black
    green, white, blue
    .
    .
    .
    and on and on, taking 3 marbles at a time out of your total of 5 marbles. The nPr is the total number of such permutations
     
  9. Apr 29, 2015 #8

    Ray Vickson

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    It means "(ordered) groups of r". I don't think the "at a time" part is particularly descriptive.
     
  10. Apr 29, 2015 #9

    s3a

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    This was exactly what I was looking for!

    This wasn't exactly what I was looking for, but it did help me understand something related that I read online.

    Thank you both! :)
     
  11. Apr 30, 2015 #10

    haruspex

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    I would say that the significance is that it denies replacement. On the other hand, it does tend to suggest no interest in the order, so it is a bit strange that it is used in the context of permutations.
     
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