# Permutations vs. combinations

Discussion in 'Math' started by boks, Jan 6, 2009.

1. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
What's the difference between these two:

1) The number of permutations of n distinct objects taken r at a time is $\frac{n!}{(n-r)!}$

and

2) The number of combinations of n distinct objects taken r at a time is $\frac{n!}{r!(n-r)!}$

?

2. ### hgmjr Moderator

Jan 28, 2005
9,030
214
You have surely already noticed that:

since permutations = $\frac{n!}{(n+r)!}$

and combinations = $\frac{1}{r!} *\frac{n!}{(n+r)!}$

then combinations = permutations time $\frac{1}{r!}$

hgmjr

3. ### steveb Senior Member

Jul 3, 2008
2,433
469
Can you be more specific as to what you are trying to understand.

$\frac{n!}{(n-r)!}-\frac{n!}{r!(n-r)!}$

Surely, that is not what you mean. Are you trying to undrstand what the definitions of permutations and combinations are?

4. ### Mathematics! Senior Member

Jul 21, 2008
1,022
4
permutations - order does matter in counting ABC is different then BCA

combinations - order doesn't matter if you have to choose 2 elements out of 5 elements.

Example {A,B,C,D,E} you don't count {A,B,C} different from {B,A,C}
They are the same

But permutations would consider them both different and count as 2 .

5. ### intrepid_atom New Member

Feb 21, 2009
1
0
To support Mathematics!

combinations = "select"
Ex: In how many ways you can select 3 letters from A,B,C,D,E?
5!/(3!2!)
permutations = "select and arrange"
Ex: In how many ways you can select 3 letters from A,B,C,D,E and then arrange those 3 letters?
5!3!/(3!2!) = 5!/2!

6. ### jamesprx Guest

Permutation is usually understood to be a sequence containing each element from a finite set once..

Combination is arrangment of elements in any order, to get different possible sequences