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# nPr and nCr

Posts: 777Registered User Member
edited January 2011
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
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## Replies to: nPr and nCr

• Posts: 146Registered User 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.
• Posts: 777Registered User Member
yeah but how do you determine when order matters. i dont really understand that cocept
• Posts: 4,706Registered User 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?
• Posts: 146Registered User 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
• Posts: 172Registered User Junior Member
nPr = n! / ((n-r)!)

nCr = n! / ((n-r)!*r!)
• Posts: 746Registered User 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.
• Posts: 1,267Registered User Senior Member
I wouldn't be surprised if either showed up. Permutation is a more natural concept for our minds I think.
• Posts: 1,012Registered User Member
Do you guys know any sites or specific pages in the blue book where I can practice these types of questions?
• Posts: 408Registered User Member

#people/things nCr #of spots

but if order matters then

#people/things nPr #of spots
• Posts: 1Registered User 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.
• Posts: 73Registered User 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.

However...

-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.
• Posts: 2,039Registered User 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?
• Posts: 2,039Registered User 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

35
• Posts: 206Registered User 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.
• Posts: 237Registered User Junior Member
Thank you for the nCr problem. Can you give an nPr problem?
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