Combination Problem: Selecting 6 Roses of 3 Colors

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SUMMARY

The problem involves selecting 6 roses from a total of 10 varieties, specifically 3 pink, 5 red, and 2 yellow, ensuring that at least one rose of each color is included in the selection. The solution requires the application of combinatorial mathematics, particularly the principle of inclusion-exclusion. By calculating the total combinations and subtracting the cases that do not meet the color requirement, the total number of valid selections can be determined.

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  • Understanding of combinatorial mathematics
  • Familiarity with the principle of inclusion-exclusion
  • Basic knowledge of binomial coefficients
  • Ability to perform calculations involving combinations
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  • Study the principle of inclusion-exclusion in combinatorics
  • Learn how to calculate binomial coefficients
  • Explore advanced combinatorial problems involving color restrictions
  • Practice solving similar selection problems with different constraints
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Mathematicians, students studying combinatorics, and anyone interested in solving complex selection problems involving multiple categories.

cyeokpeng
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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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