# How do you denote the combinations/permutations (and number thereof) of a set?

I know the formula for the number of combinations/permutations given r items and k spaces, however, I do not know how to denote the combinations or permutations, or number of combinations or permutations, of an actual set. That is, I've learned the formulas independently, as separate abstract entities, but I do not know how to actually apply the formulas.

My thinking is that since A set can be specified by a variable, and the combination and permutation formula can be abbreviated as nCk and nPk respectively, then the number of combinations and permutations for the set S = SnCk and SnPk respectively, though am not sure if this is standard convention. Also, I do not know how combinations themselves are denoted, but I imagine that there's a formula, whereby the variable S is replaced with the preferred variable in the application of said formula.

• For combinations the binomial coefficient "nCk" is commonly shown as $\binom{n}{k}$, for which the $\LaTeX$ expression is \binom{n}{k}. – hardmath Jan 22 '17 at 19:52
• Yes, but this is only practical for those versed in Latex, whereby most people are not. – Jim Jam Jan 22 '17 at 19:54
• We commonly refer to the subsets of $S$ of size $k$ as the $k$-subsets of $S$. In the sense that these "combinations themselves" are sets, set notation is commonly used to express them. – hardmath Jan 22 '17 at 19:54
• Surely you are asking for what the conventional notation is? If you want to use a novel notation, of your own invention, that is acceptable provided you include the definition of such notation in each writing that uses it. For an introduction to using $\LaTeX$ here, see how to post mathematical expressions. – hardmath Jan 22 '17 at 19:57
• When you say 'k subsets of S', how would one specify whether their subsets containing combinations or permutations? – Jim Jam Jan 22 '17 at 20:01