Combination Problem: Selecting 6 Roses of 3 Colors

Thread starter cyeokpeng
Start date Nov 16, 2005
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Combination

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To solve the combination problem of selecting 6 roses from 3 colors while ensuring at least one of each color is included, start by determining the total combinations without restrictions. Then, apply the principle of inclusion-exclusion to account for the requirement of having at least one rose of each color. Consider cases where one or more colors are excluded and subtract those from the total. The final calculation will yield the number of valid combinations that meet the criteria. This approach ensures that all color requirements are satisfied in the selection process.

Nov 16, 2005

cyeokpeng

I got this problem, don't know how to solve.

Of 10 variety of roses, 3 are pink, 5 are red and 2 are yellow. Calculate the number of ways in which we can select 6 roses, so that in the selection, at least one rose of each color is included.

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Nov 16, 2005

Tide

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Homework Helper

What, exactly, have you tried so far?

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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