Combinations of Selecting Students

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SUMMARY

The problem involves selecting 2 females and 3 males from a class of 30 students, comprising 20 females and 10 males. The solution utilizes combinatorial mathematics, specifically the combination formula, denoted as "nCr". The calculations yield 20C2 for females and 10C3 for males, leading to a total of 22,800 combinations when applying the multiplication principle. This confirms the understanding of combinatorial selection processes.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with the combination formula (nCr)
  • Knowledge of the multiplication principle in probability
  • Basic skills in solving combinatorial problems
NEXT STEPS
  • Study the combination formula in depth (nCr) and its applications
  • Explore advanced combinatorial problems involving larger datasets
  • Learn about permutations and how they differ from combinations
  • Investigate real-world applications of combinatorial mathematics in statistics
USEFUL FOR

Students in mathematics, educators teaching combinatorial concepts, and anyone interested in probability theory and its applications in real-world scenarios.

Of Mike and Men
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Homework Statement


In how many ways can 2 females and 3 males be selected from a class of 30 with 20 female and 10 male students?

Homework Equations

The Attempt at a Solution


I saw this as a two step process. Step 1 being I have N1 ways of choosing 2 females and step 2 N2 ways of choosing 3 male. This means I can apply the multiplication principle using N1*N2.

I have 20C2 ways for the female and 10C3 for the males. Using the multiplication principles I get (20C2) * (10C3) = 22,800 ways.

I'm fairly confident in my answer, I just want to be sure I'm understanding the concepts behind it, thanks.
 
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You are correct.
 
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