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

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In summary, the largest value of C(n,m) depends on the definition of the binomial coefficient and the specific values of n and m. If n and m are any positive integers with m <= n, there is no largest value. However, if n is fixed and m varies, the pattern of Pascal's triangle can help determine the largest value. The answer may also vary based on whether n is even or odd.
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for C(n, m), what values of n and m make C the largest?
 
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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.
 
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thank you!
 

What is C(n, m)?

C(n, m) is a mathematical function that represents the number of possible combinations of m items from a set of n items. This is also known as the combination formula.

How is C(n, m) calculated?

The formula for C(n, m) is n! / (m! * (n-m)!), where n! represents n factorial (n * (n-1) * (n-2) * ... * 2 * 1). This formula can also be written as nCm or n choose m.

What does it mean when C(n, m) is the largest?

When C(n, m) is the largest, it means that the given combination of n and m yields the highest number of possible combinations. In other words, it represents the most efficient way of selecting m items from a set of n items.

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

The values of n and m that make C(n, m) the largest are when n is equal to m or when m is equal to 0. In other words, when we are selecting all the items from the set (n = m) or when we are not selecting any items (m = 0), there is only one possible combination and thus C(n, m) is the largest.

What is the significance of C(n, m) in real-world applications?

C(n, m) has many real-world applications, such as in probability, statistics, and combinatorics. It is used to calculate the number of ways a specific event can occur, or the number of possible outcomes in a given scenario. It is also used in fields such as genetics, where the number of possible gene combinations can be calculated using C(n, m).

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