Combination problem, what's wrong with my reasoning?

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In summary, there are 216 ways to form a team by choosing 4 persons among 4 women and 7 men, with at least 2 women in the team. However, this solution is incorrect as it counts some teams more than once. Therefore, the actual number of ways to form the team is less than 216.
  • #1
fishingspree2
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Form a team by choosing 4 persons among 4 women and 7 men. You need at least 2 women in the team. How many ways to do it?

My solution:
1. Choose 2 women among the 4 availaible women. There is 2C4 ways of doing it.
and
2. Choose 2 persons among the 9 remaining people, there is 2C9 of doing it.

2C4 * 2C9 = 216 ways.

This is wrong, but I can't see why...
 
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  • #2
hi fishingspree2! :smile:
fishingspree2 said:
This is wrong, but I can't see why...

because you're counting some teams more than once

eg if the team contains exactly 3 women, A B and C, then you're counting that team 3 times:

once for A and B being chosen first, once for B and C, and once for C and A :wink:
 

1. What is the combination problem?

The combination problem, also known as the problem of the unity of the proposition, is a philosophical and logical issue related to the concept of propositions. It raises questions about how individual concepts or ideas can be combined to form a meaningful proposition.

2. What is the main issue with the combination problem?

The main issue with the combination problem is that it challenges the traditional view that propositions are composed of individual concepts or ideas. It questions whether there is a coherent way to combine these concepts into a meaningful proposition.

3. Can you provide an example of the combination problem?

One example of the combination problem is the statement "the unicorn is pink." This statement combines the concept of a unicorn and the color pink. However, since unicorns do not exist in reality, it raises questions about the truth value of the proposition and how these concepts can be meaningfully combined.

4. How has the combination problem been addressed by philosophers?

There have been various attempts to address the combination problem by philosophers. Some have proposed that propositions are not composed of individual concepts, but rather they are primitive and cannot be broken down any further. Others have suggested that propositions are not static entities, but rather they are dynamic processes that are constantly changing.

5. What are some potential implications of the combination problem?

The combination problem has implications for fields such as logic, philosophy of language, and metaphysics. It challenges our understanding of how language and thought work, and can also have implications for our understanding of reality and the nature of existence.

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