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

  1. Nov 6, 2005 #1
    for C(n, m), what values of n and m make C the largest?
     
  2. jcsd
  3. Nov 6, 2005 #2

    HallsofIvy

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

    If it is the binomial coefficient, [itex]\frac{n!}{m!(n-m)!}[/itex], 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.
     
  4. Nov 7, 2005 #3
    thank you!!!
     
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