4 girls bought 8 pullovers (every girl bought 2 pullovers). In How many ways they could buy the pullovers?

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- Jun 3rd 2010, 12:02 PMthe princeCombinatorics
4 girls bought 8 pullovers (every girl bought 2 pullovers). In How many ways they could buy the pullovers?

- Jun 3rd 2010, 12:04 PMundefined
See this thread.

Edit: After reading Plato's post, I realize that I made some assumptions about your intended meaning. Please do clarify. - Jun 3rd 2010, 12:11 PMPlato
There is not enough clarity in your question to begin to answer it.

Are there exactly eight pullovers? Are they all different?

Or are there many (how many) different pullovers to choose from?

If so, can a girl buy two of the same type pullover?

Can you clarify this question? - Jun 3rd 2010, 05:24 PMoldguynewstudent
The way I interpret your problem is that you have 8 different pullovers and you need to distribute them to 4 different girls so that every girl gets two pullovers. If that is the case, would the following then be correct?

The first girl would have $\displaystyle \left({8\atop 2}\right)$ ways to have the pullovers distributed to her. The second girl would have $\displaystyle \left({6\atop 2}\right)$ ways to have the pullovers distributed to her. The third girl would have $\displaystyle \left({4\atop 2}\right)$ ways and the last girls would have $\displaystyle \left({2\atop 2}\right)$. This would be 28+15+6+1.

Experts please let me know if this is correct.