Order Matter vs Doesn't Matter ( Combinatorics)

[Abdulla]

When order matter :
1- using numbers.
2- not dividing by the repeated letters.

When the order doesn't matter:
1- using letters. (i.e Yes & No)
2- dividing by the repeated letters.

I'm confused with this approach because in some cases although the order doesn't matter, we're still not dividing by the repeated letters.WHY?

Can someone clarify it to me or explain an easier approach?

[RonPurewal]

When order matter :
1- using numbers.
2- not dividing by the repeated letters.

When the order doesn't matter:
1- using letters. (i.e Yes & No)
2- dividing by the repeated letters.

I'm confused with this approach because in some cases although the order doesn't matter, we're still not dividing by the repeated letters.WHY?

Can someone clarify it to me or explain an easier approach?

i think part of the problem here is that you're looking for the clues as to whether "order matters" in your own method. this is backward reasoning: you're apparently choosing a solution method more or less blindly, and then looking at that method to see whether "order matters".
needless to say, this is not solid reasoning.

you need to look AT THE PROBLEM to tell whether order matters.
as i mentioned in this post, as well as in the post to which it links, "order matters" is a shorthand way of saying that you get a different result if you switch around the elements of the chosen set.

examples:

* if you're choosing a three-person committee from some larger group, then you can switch around the members of the committee and still have the same committee: e.g., a committee consisting of james, paul, and annie is the same as a committee consisting of paul, annie, and james. therefore, "order doesn't matter" in this case, so you'll have to divide your result by 3!.

* if you're choosing a president, vice-president, and secretary from some larger group, then you cannot switch around the three people: e.g., choosing james for president, paul for v.p., and annie for secretary is not the same as choosing paul for president, annie for v.p., and james for secretary. therefore, "order matters" in this version.

remember, the problem determines the method. the method doesn't determine the problem.