How Do You Calculate Different Combinations for Committee Selections?

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SUMMARY

The discussion focuses on calculating combinations for selecting committee members from a class of 70 students. The first part of the problem is solved using the combination formula, resulting in 70C5 for the total number of samples. For the second part, which involves assigning different roles to each committee member, the correct approach is to use the permutation formula, specifically 70P5, rather than the incorrect combination approach initially suggested.

PREREQUISITES
  • Understanding of combinatorial mathematics
  • Familiarity with the combination formula (nCr)
  • Knowledge of the permutation formula (nPr)
  • Basic factorial calculations
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  • Study the differences between combinations and permutations
  • Learn how to apply the permutation formula (nPr) in practical scenarios
  • Explore advanced combinatorial problems involving roles and restrictions
  • Practice solving problems using the combination formula (nCr) with larger datasets
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Students in mathematics, educators teaching combinatorial concepts, and anyone involved in statistical analysis or decision-making processes requiring committee selections.

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Homework Statement



We need to select 5 committee members form a class of 70 students.
  • How many possible samples exists?
  • How many possible samples exists if the committee members all have different roles?

Homework Equations



nCr = n! / (r!(n-r)!)

The Attempt at a Solution



I am able to solve the first part.
"How many possible samples exists?" = 70C5

But I am unsure of the second.
Would it simply be:
70C1 x 69C1 x 68C1 x 67C1 x 66C1 x 65C1
 
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Second part is very close. I think you understand it but made a mistake when writing it down.
 
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jz92wjaz said:
Second part is very close. I think you understand it but made a mistake when writing it down.

My mistake, 65C1 should not be there.
 

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