Is one form of the answer more right than the other

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Sigma notation allows us to write sums in a more general form, so that we don't have to write out every single term. It is a common notation used in mathematics and statistics.So, in summary, the problem asks for the number of ways to select 12 people from a group of 10 men and 10 women, where there must be an even number of women. Your answer and the answer key both give equivalent solutions, with the answer key utilizing sigma notation to write the sum in a more compact and general form. While your answer is not technically incorrect, the answer key's solution is more concise and efficient.
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find_the_fun
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A committee of 12 is to be selected from 10 men and 10 women. In how many ways can the selection be carried out if there must be an even number women?

I answered \(\displaystyle {10 \choose 2}{10 \choose 10}+{10 \choose 4}{10 \choose 8}+{10 \choose 6}{10 \choose 6}+{10 \choose 8}{10 \choose 4}+{10 \choose 10}{10 \choose 2}\)

The answer key gives

\(\displaystyle \sum\limits_{i=1}^5 {10 \choose 12-2i}{10 \choose 2i}\)

I can see how the two are equivalent but is one more correct than the other? I found the first answer just by thinking about it; was the second answer arrived at by applying a formula I'm unaware of? i.e. does the second answer imply a certain approach?
 
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Re: is one form of the answer more right than the other

I have moved the topic, as this type of counting problem is the type typically encountered in an introductory statistics course.

Your answer is not quite correct. Can you spot the missing term?

Your answer key is taking advantage of sigma notation which can make writing sums much more compact.
 

FAQ: Is one form of the answer more right than the other

What does it mean for one form of the answer to be "more right" than the other?

The concept of one form of the answer being "more right" than the other can vary depending on the context. In general, it refers to one answer being more accurate, precise, or supported by evidence than the other. However, the definition of "more right" can also be subjective and influenced by personal beliefs or biases.

Can there be multiple "right" forms of the answer?

Yes, there can be multiple forms of the answer that are considered "right". This can occur when the question is open to interpretation or when there are multiple valid solutions or explanations for the answer.

How do scientists determine which form of the answer is more right?

Scientists use various methods to determine which form of the answer is more right. This can include conducting experiments, analyzing data, and reviewing existing research and evidence. Ultimately, the form of the answer that is supported by the most reliable and consistent evidence is considered to be more right.

Is one form of the answer always more right than the other?

No, one form of the answer is not always more right than the other. It is important to consider the context, available evidence, and potential biases when determining which form of the answer is more right. Additionally, new evidence or advancements in research can change which form of the answer is considered to be more right over time.

How does the concept of one form of the answer being more right apply to scientific theories?

Scientific theories are based on evidence and are constantly evolving as new evidence is discovered. Therefore, the concept of one form of the answer being more right can apply to scientific theories. However, it is important to note that all scientific theories are considered to be "right" in the sense that they are supported by evidence and have been thoroughly tested and validated by the scientific community.

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