Order matters, order doesn't matter, combinations and permutations?

Question

Hi, I've been through practically every single entry there was on combinations and permutations. However, all the answers go about saying permutations , order matters, combinations, order doesn't matter. What I'm confused about is WHAT IS THE ORDER people are talking about...any explanations?

Answer 1

It means the order of the items being chosen.

Suppose you had the items a, b, c, and d, and you are asked to make combinations of three items. In that case, abc is the same thing as bca or acb. The order of the items doesn't matter, so the same items in a different order are not a unique combination. abd and bcd are different combinations because they contain different items.

Now, suppose you are instead making permutations of three items, from the same set of four items. In that case, abc is different from bca, and acb is yet a third permutation. The order of the items does matter, so when you change the order you have a different permutation. Note that abd and bcd are also different permutations

Since order matters with permutations, you have more permutations than combinations from the same collection of items; you can reorder each combination to get a variety of new permuations.

Answer 2

Permutation Order Matters

Answer 3

When you're doing a combination, order doesn't matter. This means though that if you have 5 objects you have to divide by 5! after doing the permutation thing.

Answer 4

In combinations order does not MATTER
In permutations order matters

Ex. 123 and 231 and132 are the same combination of three
elements
But if you are speaking of permutations they are three different
permutations of the same numbers

Answer 5

suppose u have to arrange something....some number or letters or figures..
if u follow a particular order.....that is called permutation
if u follow no particular order and arrange in any way u like....it is combination...

for example,u have to arrange the letters a,b,c.
number of objects is 3, n=3
and we have to use all 3 objects, so, r=3

if u want to know in how many ways the letters can be arranged in order the answer is,
n!/(n-r)!
=3!/(3-3)!
=3!/0!
=3!/1
=6
so there are 6 different arrangements of a,b,c, which are

abc
acb
bac
cab
bca
cba
this is permutation

but if u have don't have to follow any order, you can choose any one of the arrangements from above.
so your no. of arrangement is 1, which is found by,
n!/(r!(n-r)!)
=3!/(3!(3-3)!)
=3!/(3!(0)!)
=3!/(3!*1)
=3!/3!
=1

Answer 6

12 is different from 21 (order maters)
2+1 = 3 and 1+2 = 3 (order doesn't matter)

Answer 7

I think an example will help out too...
A situation where order MATTERS is elections. A as President, B as vice president and C as secretary is not the same as B for pres, C fur VP and A for secretary. Thus, order matters.
A situation where order does not matter is when people are elected to a cabinet where everyone is equal. Then ABC is the same as CAB, and so on.

Answer 8

NON LINEAR PHILOSOPHY
Linear Philosophy, or the idea that everything that exists is connected through cause and effect to everything else that exists came into its own with DesCartes in the seventeenth century. But it is an assumption. Non Linear philosophy simply sets that assumption aside and examines the universe as connected through complex organization.