Understanding the Evolution of Binomial Coefficient Notation: Old vs. New

[YoungPhysicist]

I am learning binomial theorem now on my long journey to calculus. I noticed that in older textbooks, the binomial coefficient looks like

C(n on top,k on bottom)
I don’t think that I can display it here

and in newer ones,they look like
$\binom{n}{k}$

is the old notation outdated?or this is just author problems and has nothing to do with old books and new books?

 

[DrClaude]

Wikipedia lists the many different notations: https://en.wikipedia.org/wiki/Binomial_coefficient#History_and_notation

It is usually a preference of the author which to use.

 

[YoungPhysicist]

Wikipedia lists the many different notations: https://en.wikipedia.org/wiki/Binomial_coefficient#History_and_notation

It is usually a preference of the author which to use.

Thanks!

 

[RPinPA]

C(n on top,k on bottom)
I don’t think that I can display it here

You mean $C^n_k$? That's just C^n_k, C superscript n, subscript k.

The notation I learned and tend to use most often is $nCk$, especially in expressions like card-counting problems (Ex: what is the probability of drawing 5 cards consisting of 3 diamonds and 2 hearts from a standard deck of cards?). Expressions made of multiple binomial coefficients in other words.

I've also seen $C(n,k)$ fairly often. I think that is often used in elementary classes such as high-school algebra.

 

[mathman]

Latex seems to lean towards $\binom{n}{k}$.

 

[YoungPhysicist]

You mean $C^n_k$

That don’t actually look like the actual one.I am awared of the sup/subscript method you just mention,but still a viable way.