# Writing expressions using permutations versus combinations

This question states a PMF using combination notation, and the numerator of the expression is actually equal to a permutation: $$\frac{\binom{365}{k}k!}{365^k}$$

I have been trying to write permutations using latex, and I find that it is quite awkward. Question: Is the math written in combinations because that is the preferred option to express the logic or because permutations are difficult to create in LaTeX/Stackexchange.

Note: You might think this trivial, but I am trying to understand. Should I think in "combinations" or "permutations"?

• In the numerator we are counting ordered sequences of $k$ different elements out of $365$ and the expression clearly tells the story of how we counted them: choose the elements, and then choose their ordering. There may be other ways to write it, and the ones I can think of do not seem any better/worse nor more/less awkward in LaTeX, in my opinion. Maybe this one is convenient in the given context. Feb 21 at 10:28
• I am not able to use permutations in stackexchange. Could you give me some links that do. Would like to learn. Feb 21 at 10:32

The count for distinct permutations of $$k$$ elements selected from a set of $$n$$ is equal to the count for distinct combinations of $$k$$ elements selected from $$n$$ times the count for distinct arrangements of those $$k$$ elements.

$${^n\mathrm P_k}={^n\mathrm C_k}~k! = \dbinom n k~k! = \dfrac{n!}{(n-k)!}$$

{^n\mathrm P_k}={^n\mathrm C_k}~k! = \dbinom n k~k! = \dfrac{n!}{(n-k)!}

Use whichever format you prefer. There isn't that much difference in mathjax complexity.

If needed many times in your text, you could always use \def\perm#1#2{{^{#1}\mathrm P_{#2}}} to define an inline macro replacement, so \perm n k produces the required symbols as often as needed.

$$\def\perm#1#2{{^{#1}\mathrm P_{#2}}}\perm n k$$

It depends on the nature of the problem.

In the supplied expression, Combination notation, as you’ve written it, is more appropriate.

Combinations are used when the order of selection doesn’t matter, hence Permutations when the order does matter. So, it isn’t a function of ease either using Tex or just a preference.

So, when focusing on lists of elements where their order matters, you would use Permutations.

When your focus is on groups of elements where the order does not matter, you would use. Combinations.