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nPr and nCr

AndrassyAndrassy Registered User Posts: 777 Member
edited January 2011 in SAT Preparation
Could someone explain the difference for me and maybe give an example? nPr is where the probability must be done in a certain way and nCr is any way? i dont really understand this. could someone explain please =)
Post edited by Andrassy on

Replies to: nPr and nCr

  • xantixgravityxxantixgravityx Registered User Posts: 146 Junior Member
    uh i'm not sure how you guys say it in english but nPr is for permutation (?) which is the probability when the order matters.
    nCr is combination, which is the probability when the order does not matter.
  • AndrassyAndrassy Registered User Posts: 777 Member
    yeah but how do you determine when order matters. i dont really understand that cocept
  • lil_killer129lil_killer129 Registered User Posts: 4,706 Senior Member
    How do you even remember that permutation = matter orders. I always get confused about which is which. Is there a device I can use to memorize that?
  • xantixgravityxxantixgravityx Registered User Posts: 146 Junior Member
    not really...the words in the problem say it.
    for example, if you have to find how many diff 'combinations' you can get of 3 out of 12 pizza toppings , then that's just combination because the order in which you put the toppings doesn't matter.
    however, if it's a problem like this: in how many ways can be chosen a president, vice president and secretary from a group of 30 students? in this case order does matter since it's not the same choosing a president and choosing a vice president.
    i hope you understood, i translated these examples from my math in spanish book. :S
  • BoridiBoridi Registered User Posts: 172 Junior Member
    nPr = n! / ((n-r)!)

    nCr = n! / ((n-r)!*r!)
  • gcards1gcards1 Registered User Posts: 746 Member
    I'm pretty sure only one of them ever shows up on the SAT (from a crap load of practice test experience and two real tests +psat). I think it's nCr. I could be wrong.
  • chibearsfan17chibearsfan17 Registered User Posts: 1,267 Senior Member
    I wouldn't be surprised if either showed up. Permutation is a more natural concept for our minds I think.
  • IcerIcer Registered User Posts: 1,012 Member
    Do you guys know any sites or specific pages in the blue book where I can practice these types of questions?
  • RabidchickensRabidchickens Registered User Posts: 408 Member
    Just use your TI83

    #people/things nCr #of spots

    but if order matters then

    #people/things nPr #of spots
  • bitbucketbitbucket Registered User Posts: 1 New Member
    nCr : Out of N, Choose R : Just Choose, When I choose I don't care about order.

    Or you can remember that permute means "change the order of".

    In addition remember that there will certainly be more ways in which to do things when order matters, hence when you permute, you lose one of the terms in the denominator, thus yielding a larger number of options when you permute.
  • jiieunjiieun Registered User Posts: 73 Junior Member
    I usually remember it like this:

    -Use nPr when order matters. For example, imagine stacking scoops of ice cream in an ice cream CONE. You can choose to put chocolate, vanilla, and strawberry in a certain order since the cone only stacks one way.


    -Use nCr when order does NOT matter. For example, imagine placing scoops of ice cream in a BOWL. Here, the order does NOT matter because you can place the ice cream in the bowl without stacking them on top. You can just get different combinations in the bowl without worrying about the order.
  • GreedIsGoodGreedIsGood Registered User Posts: 2,039 Senior Member
    Here is a practice question:

    I have 7 different colored marbles. I choose 4 from the bag. How many different possibilities are there?
  • GreedIsGoodGreedIsGood Registered User Posts: 2,039 Senior Member
    First marble can be any of the 7.
    Second marble can any of the 6 remaining marbles.
    Third " " " 5
    Fourth " " " 4

    Hence: 7*6*5*4 =30*28 = 840

    But wait, I am overcounting!

    Divide by 4!=4*3*2=24

  • SubsidizeSubsidize Registered User Posts: 206 Junior Member
    Combinations are often used for choosing members of a committee that has no hierarchy, versus choosing people for president, vice president, secretary slots in a club.
  • blob793blob793 Registered User Posts: 237 Junior Member
    Thank you for the nCr problem. Can you give an nPr problem?
This discussion has been closed.