1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Why is nPr called [. . .]?

  1. Apr 29, 2015 #1

    s3a

    User Avatar

    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

    User Avatar
    Gold Member

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

    s3a

    User Avatar

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

    SteamKing

    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    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

    User Avatar
    Gold Member

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

    s3a

    User Avatar

    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

    User Avatar
    Gold Member

    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

    User Avatar
    Science Advisor
    Homework Helper

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

    s3a

    User Avatar

    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

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted