Solve Combination Problem: Choose 4 Shoes from 5 Pairs

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To solve the problem of choosing 4 shoes from 5 pairs without selecting a complete pair, one must first recognize that only 5 individual shoes are available for selection. The solution involves using combination formulas to determine the number of ways to select 4 shoes from these 5. The key is ensuring that no two shoes come from the same pair, which simplifies the selection process. The discussion emphasizes the importance of showing previous attempts to facilitate better guidance. Ultimately, the focus is on applying permutation and combination principles to arrive at the correct answer.
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Homework Statement



A closet has 5 pairs of shoes. The number of ways in which 4
shoes can be chosen from it so that there will be no complete pair are?

Homework Equations



Permutation and Combination formulae

The Attempt at a Solution



I tried but couldn't figure it out anyway.
 
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It would be a lot easier for us to tell you what you did wrong, if you showed us what you did.
 
Since you don't want to have a pair you are only left with 5 shoes to pick from. Now choose 4 from that.
 

Thread 'Family of lines that are at a distance of 5 from the origin'

I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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