For C(n, m), what values of n and m make C the largest?

[asdf1]

for C(n, m), what values of n and m make C the largest?

 

[HallsofIvy]

Well, that depends a lot on what C(n,m) means!

If it is the binomial coefficient, $\frac{n!}{m!(n-m)!}$, then the answer depends on precisely what you are asking. If I take your question literally: that n and m can be any positive integers (m<= n) there is no answer: taking n larger and larger gives larger and larger values for C(n,m). There is no largest value.

If you mean "for a specific n, what value of m makes the binomial coefficient C(n,m) largest", write a few rows of Pascal's triangle and the pattern should become obvious. A precise answer then will depend on whether n is even or odd.

 

[asdf1]

thank you!