Difference btw. nCr and nPr

Discus: SAT/ACT Tests and Test Preparation: April 2004 Archive: Difference btw. nCr and nPr
 By Miumiu016 (Miumiu016) on Friday, April 30, 2004 - 07:30 pm: Edit

Could someone explain the difference between 7 C 2 and 7 P 2, and an example (a situation) using both? Thanks.

 By Lisasimpson (Lisasimpson) on Friday, April 30, 2004 - 07:36 pm: Edit

ok this took me like half of yesterday to figure out

7 C 2 would be when order doesnt matter. like if you have 7 different seeds and want to plant 2 in your garden, then apple seed, orange seed would be the same as orange seed, apple seed

7 P 2 would be when order does matter. like if you're looking for letters on a license plate. PS would be different from SP

yea, i dunno if that makes any sense, but thats all i got out of lookin it up

 By Tinkerchelle (Tinkerchelle) on Friday, April 30, 2004 - 07:48 pm: Edit

that's correct. C is combination...for example, if you were picking people to be in a group, it doesn't matter what order they are picked in... 8C2 means two people out of eight.

however, in permutations order matters: if you were doing the number of ways a randomizer on a playlist could put 12 songs into sets of four, then order would matter, and so it would be 12 P 4

 By Number9 (Number9) on Friday, April 30, 2004 - 07:52 pm: Edit

I always remembered that a combination on a lock was really a permutation (order matters), and I never mixed the two up.

 By Miumiu016 (Miumiu016) on Friday, April 30, 2004 - 07:52 pm: Edit

Thanks Tinker and Lisa.

 By Valk78 (Valk78) on Friday, April 30, 2004 - 09:45 pm: Edit

umm isnt Combinations when order matters !! and permutations when it doesnt!! , do it on your calculator.... nCr yeilds a smaller answer than does nPr, so that would mean nCr order matters. Am i missing something ?

 By Lahlahlah (Lahlahlah) on Friday, April 30, 2004 - 09:50 pm: Edit

omfg
u guys are dumb
nCr is comboniation
n!/((n-r)!r!)
nPr is permuations order matters
n!/(n-r)!

 By Crypto86 (Crypto86) on Friday, April 30, 2004 - 09:50 pm: Edit

Actually that would happen. Think about it - if you have 3 items to put in order (A,B,C) and ABC is the same as CBA for combinations, but ABC is different from CBA in permutations, it would make sense that there are more permutations than combinations (more possibilites to choose from).

 By Fusiachi (Fusiachi) on Friday, April 30, 2004 - 11:41 pm: Edit

In a combination, order doesn't matter.

n!/(n-r)! r!

Permutations are when order matters.

n!/(n-r)!