Hi,

Wasn't sure if this belonged in Intermediate or Beginning Algebra. Apologies if this is misplaced.

I've been playing around with the formula for Combinations (n!/(n-r)!*r!) and was trying to answer the question: from the set n of 26 letters of the alphabet, for what value of r is the possible number of sets the greatest.

At first I thought it would be either 1 or 26 but discovered that not to be the case. As I tried more values I discovered a symmetrical pattern around the midpoint of 13, which I thought was interesting. I then wanted to try to graph that on my graphing calculator but I'm struggling to convert the Combination formula above into an equation of the form y=ax^2 + bx + c, (where n=x, r=y) which is the form I'm assuming would be needed.

If that's the correct form needed to graph it then I'm struggling with doing the algebraic manipulation to get it into that form.

Am I missing something?