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 =)
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.
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
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.
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.
-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.
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.
Replies to: nPr and nCr
nCr is combination, which is the probability when the order does not matter.
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
nCr = n! / ((n-r)!*r!)
#people/things nCr #of spots
but if order matters then
#people/things nPr #of spots
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.
-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.
I have 7 different colored marbles. I choose 4 from the bag. How many different possibilities are there?
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