Sign Up For Free

**Join for FREE**,
and start talking with other members, weighing in on community polls,
and more.

Also, by registering and logging in you'll see fewer ads and pesky welcome messages (like this one!)

- Reply to threads, and start your own
- Create reports of your
**campus visits** - Share college
**photos**and**videos** **Find your dream college**, save your search and share with friends- Receive our
**monthly newsletter**

Home
/
College Discussion / College Admissions and Search / SAT and ACT Tests & Test Preparation / SAT Preparation

Andrassy
Posts: **777**Registered User Member

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

146Registered User Junior MembernCr is combination, which is the probability when the order does not matter.

777Registered User Member4,706Registered User Senior Member146Registered User Junior Memberfor 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

172Registered User Junior MembernCr = n! / ((n-r)!*r!)

746Registered User Member1,267Registered User Senior Member1,012Registered User Member408Registered User Member#people/things nCr #of spots

but if order matters then

#people/things nPr #of spots

1Registered User New MemberOr 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.

73Registered User Junior Member-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.

2,039Registered User Senior MemberI have 7 different colored marbles. I choose 4 from the bag. How many different possibilities are there?

2,039Registered User Senior MemberSecond marble can any of the 6 remaining marbles.

Third " " " 5

Fourth " " " 4

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

840But wait, I am overcounting!

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

35206Registered User Junior Member237Registered User Junior Member