+130466 Re: what is a combination
It represents the number of sets (or subsets) that we can form by selecting "r" things from "n" things. Here's an example...let's suppose we have a set of 3 objects labeled "A," "B," and "C."
Note that I can "choose" all three obejcts to form one set, namely, {A,B,C} The braces denote that we're talking about a set of things.
Or, I could choose any two of the objects. This would give us {A,B}, {A.C} and {B,C}.....note that the "order" of things in the set doesn't matter in combinations.
Or, I could choose any one of the objects from the three...this gives us {A}, {B}, {C}.
There is one more way to form a "set" of these objects......this may seem strange....DON"T CHOOSE ANY OF THEM!!! This is known as the "empty" set and is just denoted as { } or as Ø.
Note the number of sets we've formed = 2^(n things) = 2^(3) = 8.
Since it's cumbersome to try and figure how many sets can be formed by selecting some number of objects from a large number of them, we have a "formula" to do that.
It's denoted by C(n,r) or nCr.......both things are used......and it tells us how many sets can be formed by choosing 'r" things from "n" things. Note that n is always greater than or equal to r....That makes sense.....I couldn't choose 6 things from just 3 !!!!
The "formula" is.... (n!) / [(n-r)! (r!)].......where "r" is the number of objects chosen from "n" things.
The " ! " is known as a "factorial" or just "factorial."
I'll spare you the "fancy" definition of this, but it's really just the product of "n" (or "r") and all the positive integers less than "n' or "r." For example, if "n' (or "r') = 3, then 3! = 3 x 2 X 1 = 6. (Note a "special case"..... 0! = 1)
So, looking at our example, let's suppose that we wanted to know how many sets we could form by choosing 2 things from 3. By the "formula," we have C(3,2) =
(3!) / [(3-2)! (2!)] = ( 3!) / (1)! (2!) = (3X2x1) / [(1) * (2X1)] = 6/2 = 3 .....which is exactly what we found!!
Combinations are used extensively in statistics and probability. Another thing that is sometimes encountered is the "permutation." It, unlike the combination, DOES take into account "order" within sets. Thus, in a permutation, {A,B} ≠ {B,A} In general, the "permute" of something is usually greater than a "combination" of that something....but not always!!!
I hope this helps..... 
+33654 A combination is the arrangement of a number of objects from a group such that the order of the arrangement doesn't matter.
+130466 Re: what is a combination
It represents the number of sets (or subsets) that we can form by selecting "r" things from "n" things. Here's an example...let's suppose we have a set of 3 objects labeled "A," "B," and "C."
Note that I can "choose" all three obejcts to form one set, namely, {A,B,C} The braces denote that we're talking about a set of things.
Or, I could choose any two of the objects. This would give us {A,B}, {A.C} and {B,C}.....note that the "order" of things in the set doesn't matter in combinations.
Or, I could choose any one of the objects from the three...this gives us {A}, {B}, {C}.
There is one more way to form a "set" of these objects......this may seem strange....DON"T CHOOSE ANY OF THEM!!! This is known as the "empty" set and is just denoted as { } or as Ø.
Note the number of sets we've formed = 2^(n things) = 2^(3) = 8.
Since it's cumbersome to try and figure how many sets can be formed by selecting some number of objects from a large number of them, we have a "formula" to do that.
It's denoted by C(n,r) or nCr.......both things are used......and it tells us how many sets can be formed by choosing 'r" things from "n" things. Note that n is always greater than or equal to r....That makes sense.....I couldn't choose 6 things from just 3 !!!!
The "formula" is.... (n!) / [(n-r)! (r!)].......where "r" is the number of objects chosen from "n" things.
The " ! " is known as a "factorial" or just "factorial."
I'll spare you the "fancy" definition of this, but it's really just the product of "n" (or "r") and all the positive integers less than "n' or "r." For example, if "n' (or "r') = 3, then 3! = 3 x 2 X 1 = 6. (Note a "special case"..... 0! = 1)
So, looking at our example, let's suppose that we wanted to know how many sets we could form by choosing 2 things from 3. By the "formula," we have C(3,2) =
(3!) / [(3-2)! (2!)] = ( 3!) / (1)! (2!) = (3X2x1) / [(1) * (2X1)] = 6/2 = 3 .....which is exactly what we found!!
Combinations are used extensively in statistics and probability. Another thing that is sometimes encountered is the "permutation." It, unlike the combination, DOES take into account "order" within sets. Thus, in a permutation, {A,B} ≠ {B,A} In general, the "permute" of something is usually greater than a "combination" of that something....but not always!!!
I hope this helps.....
