simple recursion help

[Hung Jung Lu]

Thorsten Kampe <thorsten at thorstenkampe.de> wrote:
> > (1) "Variation" is the same as "permutation".
> 
> Sorry, no.

Sorry, yes. Please learn to accept the fact that a word
("permutation", in this case) can have several definitions. You are
not the Pope of mathematics, and there is none. Different people
define it different ways. Your definition is by no way the only
accepted definition. You have been raised one school of
notation/terminology, other people have been raised in another school
of notation/terminology. What the French call "body" ("corps"), the
American call it "field" ("champ") as in "the Real Number Field, the
Complex Number Field". Many examples like that.

> * variations   without repetition = P(n, k)

Funny, "variation" starts with the letter "v", where do you think the
"P" as in your "P(n, k)" come from? Surely not from "Pariation",
right? The fact that you see the "P(n, k)" notation shows you that
many people call this function "permutation". You simply were raised
in a particular school of terminology and were not aware that another
school of terminology existed.

What you have called ""variation with repetition", other people call
it "string". As I said, you are not the Pope of mathematics, and don't
expect other people will agree with your terminology.

Learn to accept the fact that what you call "variation", other people
call it "permutation". Like it or not, it's a fact. Now, re-read the
following sentence:

> > (1) "Variation" is the same as "permutation".

and try to understand what I was saying:

    Your "variation" == Other people's "permutation"

is that clear, now?

Please check
http://mathworld.wolfram.com/BallPicking.html
which I have pointed out in my earlier message and which you did not
bother to read, at all. I would say the majority of students in the
U.S.A. are trained with the terminology convention I use. Surely the
usage of the term "variation" is also popular, but I would say that at
present it constitutes the minority, not the majority.

As I said, It's matter of semantics.

regards,

Hung Jung