math question

[Reel]

I am trying to write a program that involves catalan numbers. I found this web page that describes them and gives the formula. The problem is that I can't remember at all what the
( 2n )
( n )
expands out to be. I know I have seen it and used it but I never remember what it means. Can someone please tell me? thanks.

 

[Soccer55]

kCr = k!/[r!*(k-r)!]

Just apply that with k=2n and r=n

-Tom

 

[DanFungus]

Originally posted by: Soccer55
kCr = k!/[r!*(k-r)!]

Just apply that with k=2n and r=n

-Tom

I learned that as nCr...


anywho, it's basically what Soccer said.

(2n)!
____
n!*(n)!

the (n)! is that because it's (2n-n)!


oh, and in the graphing calculators (speaking on 83+ in particular, since it's the one I have) it has in Math button, left, option 4 is nCr. Or it's in the catalog too.

edit 2: What it means is that out of 2n total choices, you are picking n of them. And, the order doesn't matter. nPr would be 2n total choices, n chosen, order does matter. Order doesn't matter would be out of 5 books, choose 5 and put them on the shelf. There's 1 way to do that because they are a group of 5 books. Order does matter would be choose 5 books from 5 books, and put them on the shelf. There are 5! ways to do it, because for book that goes first, there are 5 choices, for the second, there are 4 (since one book is already in place), third place are 3 choices...and so on. Thus 120 ways to do it if order matters, compared to 1 way if order doesn't matter. Hope this helps

 

[Reel]

thanks. That answers my question but what is this thing called. I don't even remember that or I could have google'd it.

 

[DanFungus]

nCr (order = no matter) is called a Combination
nPr (order = matters) is called a Permutation