Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

I know the number of combinations is called ${}_nC_r$, but what about all the exact outcomes?

For example: I have $3$ elements $a,b,c$ and for the parameter $2$, I will have outcomes $$ab,\quad ac,\quad ba,\quad bc,\quad ca,\quad cb$$

I want to search different implementations of this, but I don't know what term should I input in google.

share|cite|improve this question
In french, this is Arrangement (see – Arnaud May 20 '13 at 9:41
That's a nice information. I don't know why that is french only though >< – Abby Chau Yu Hoi May 20 '13 at 10:09
If you look at the Wikipedia article, you could see that there is also a german word, an italian word... – Arnaud May 20 '13 at 11:05
up vote 0 down vote accepted

If I have a set $X$ with $n$ elements, and I wanted to refer one of the possible "outcomes" of choosing $k$ elements (without the order mattering), I would just call it "a $k$-element subset of $X$". Thus, the number of $k$-element subsets of $X$ is $\binom{n}{k}$ or ${}_nC_k$, depending on your notational preferences. I'm not aware of any more specialized term.

I would use the term "$k$-tuple of elements of $X$" to mean an ordered $k$-element subset of $X$ (possibly with repetitions). Thus, the number of $k$-tuples of distinct elements of $X$ is ${}_nP_k$, and the number of $k$-tuples of elements of $X$ is $n^k$.

share|cite|improve this answer
In combinatorics, I heard many different terms - variations, partial permutations, k-permutations. – Sulthan May 21 '13 at 9:45

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.